Prepare Dough. [If using instant yeast, skip to Step 3 and add the yeast and the milk (can be cold) with the rest of the ingredients.] In microwave at 20 second intervals, stirring after each interval, warm milk to body temperature, generally between 105°F and 110°F. Alternatively, you can heat the milk in a saucepan on a low flame, stirring constantly. Either way, do not let the milk get above 115°F. (If you do, just let it sit out at room temperature for a couple of minutes constantly checking it until it cools to body temperature.)
Place warmed milk into bowl of electric mixer. Sprinkle yeast and approximately 1 tsp. of the sugar over the milk. Using a fork, stir the mixture to distribute the sugar and hydrate the yeast granules. Allow to sit for approximately 3-5 minutes until the mixture gets foamy.
Add the room temperature egg, the room temperature egg yolk, and the vanilla to the mixture. Using the dough hook, turn the mixer on at a low speed and add the rest of the sugar. With the mixer running at the lowest speed, add the flour. As the flour starts to get absorbed by the liquid mixture, raise the mixer to a medium speed. You may need to turn the mixer off once or twice to wipe down the sides of the bowl with a rubber spatula. Allow to knead for approximately 3 minutes. The dough should clean the sides of the bowl and be tacky, even a bit sticky. If it is too wet (sticking to the sides and bottom of the bowl), add some flour, no more than 1 tbsp. at a time. If the mixture is too dry, add a little milk, 1 tsp. at a time.
Lower the mixer speed to low (1 or 2 on the KitchenAid) and slowly add the salt, allowing it to knead into the dough, an additional 3 minutes. Stop the mixer and take a small piece (approximately 1 tsp.) of dough and stretch it between your fingers. It should form a “window pane”, meaning it should get thin enough that it is translucent without it ripping. If it is not at that point yet, continue kneading in the machine at 1 minute intervals. (It may just need an additional minute or two to reach the window pane stage. If it still isn’t there yet, check to see if the dough is too dry. If it is, add ½ tsp. water and knead another minute.)
With the mixer running at medium speed, add the butter. It is best to add it one piece at a time, waiting until it is fully integrated into the dough before adding the next piece. You may need to turn off the mixer from time to time to push the slab of butter back into the range of the dough and the hook. This process will take approximately 5 minutes. Once all the butter is incorporated, the dough will look shiny and be slightly sticky. (If, after approximately ten minutes, the butter is still not fully incorporated, do not panic. Just move to the next step – having some unincorporated butter is not problematic in this recipe. That said, the key to incorporating the butter is nothing more than patience.)
Lightly grease a bowl with a little butter or nonstick cooking spray. Form dough into a ball and place it in the bowl. Turn the dough over to coat it in the butter or nonstick cooking spray and cover tightly with plastic wrap.** Let the dough sit in a warm area on the counter until doubled in size, approximately one hour.
Brownie Filling. In a 2 quart saucepan over the lowest heat, melt the butter and chocolate. Stir occasionally until fully melted. Remove from heat. Stir in the sugar and brown sugar. Set aside for a couple of minutes to make sure the mixture cools completely. Add the beaten egg and vanilla. Mix in the flour and salt just until all the flour is fully absorbed. Cover pot (plastic wrap will do) and refrigerate.
Prepare two loaf pans, 8 or 9 inches long, and 3 to 5 inches wide, by coating with nonstick cooking spray or butter. (Using butter imparts more flavor on the edges of your babkas.) For an even easier pan removal, use parchment paper on the bottom and/or sides of the pan, but be sure to coat the parchment with nonstick cooking spray or butter.
Once dough has doubled in size, remove the plastic wrap and de-gas it by folding it over onto itself and knead it a few times by hand. Divide it in half, preferably by weight. Cover one half with plastic wrap until you are ready to work with it.
Roll dough out to three inches longer than the length of your pan. (If you are using a 9 inch long pan, roll it out to 12 inches, to form a rectangle of 12 inches by approximately 16-18 inches. The dough should be approximately ⅛ inch thick.
Remove brownie filling from the refrigerator. Leaving a border of ½ an inch on every side, spread ½ of the brownie filling on the dough. (There should be approximately 300 g. of brownie batter, so use approximately 150 g. for each babka.)
Have the dough facing you the long way so that the side of the dough that is three inches longer than the length of your pan is facing you. For example, if your pan is 9 inches long, the side of the dough that is 12 inches long should be in front of you. Roll the dough upward so that you have a 12 inch long log. Trim ½ inch to an inch from both sides of the log. (Tip: Save these trimmings and bake in a separate greased pan with trimmings from second log. This is the “mini babka” you get to taste so you can present the two babkas to your guests and already know how good it tastes!)
Slice the log down the middle in half, exposing the layers of filling. Form an X with the two pieces, and cross the two over each other starting from the middle going down towards you. Repeat from the middle going up. Place dough in prepared pan. Cover loosely with plastic wrap and allow to sit until doubled in size, approximately one hour.
Repeat steps 10-13 with second portion of dough from step 9.
Approximately 30 minutes into the second rise, preheat oven to 350°F.
Once the babkas have doubled in size, bake for 30-35 minutes.
Towards the end of the baking time, in a small pot bring the water and sugar to a boil, stirring to ensure the sugar is fully melted. Stir in the vanilla.
The babka is done once the top is golden brown. (Best to take the babka’s temperature. It is done when the internal temperature reaches 205°F).
Immediately after removing the babkas from the oven, brush the tops with the hot syrup glaze. Return to the oven for 2 additional minutes.
Cool babkas in pans for 10-15 minutes and then remove them from their pans onto a wire rack. (Use a metal spatula or flat knife against the sides of the pans before turning the pans over.)
Once at room temperature, if not eating immediately, cover in plastic wrap. If they actually last so long, they stay fresh for several days wrapped in plastic and stored at room temperature. They also freeze beautifully, wrapped in plastic wrap, for up to 3 months.