[If using instant yeast, skip to Step 3 and add the yeast and the milk 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, the strawberry paste, 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 dough scraper or rubber spatula. Allow to knead for approximately 3 minutes. The dough should clean the sides of the bowl and be tacky, but not too 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 5-10 minutes. Once all the butter is incorporated, the dough will look shiny and be slightly tacky. (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.
Lightly spray two 8½" x 4½" loaf pans with nonstick cooking spray or grease with butter. (Using butter imparts more flavor on the edges of your brioche.) 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. Divide the half of the dough you are working with into two equal portions, shaping each into rounds. Place each round into a loaf pan. Cover loosely with plastic wrap and let rise for another hour. Repeat with remaining dough.
Approximately 30 minutes into the second rise, preheat oven to 350°F.
Once the brioche have doubled in size, beat an egg and, using a pastry brush, egg wash the tops of the brioche. Sprinkle with Swedish pearl sugar. Bake for 55-65 minutes.
Cool brioche 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. (Tip: individually wrap slices in plastic wrap prior to freezing so you can grab a slice or two whenever the craving hits.)