Dough. [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.*** Refrigerate the dough overnight.
Strawberry Cream Filling. In an airtight container, mix together the heavy cream with the diced strawberries. (These are the first two ingredients in the Strawberry Cream Filling.) Cover and refrigerate overnight. Set a a heatproof bowl aside or line a baking sheet with plastic wrap.
In a heavy saucepan, bring the milk, vanilla bean paste and half of the sugar (you can eyeball it) to a boil, stirring occasionally to make sure the sugar dissolves.
While the milk is heating, in a medium bowl, whisk together the egg, the yolks, the rest of the sugar, the freeze dried strawberry powder, and the cornstrach. Whisk until the mixture starts to thicken slightly, so it leaves a ribbon for a few seconds when you lift the whisk from the bowl. Place the bowl on a rubber mat, other non-stick surface, or wrap a wet towel around the bottom to hold it in place as you whisk in the hot milk.
Once the milk comes to a boil, remove it from the heat and allow it to cool for approximately one minute. Carefully pour approximately ⅓ of the milk mixture in the egg mixture, whisking constantly. Quickly pour the tempered egg mixture back into the pot with the rest of the milk mixture, whisking constantly. Cook over medium heat, whisking constantly. Once it starts to boil, set a timer for 2 minutes. Continue cooking and whisking constantly. After two minutes, immediately pour the pastry cream through a strainer into a heatproof bowl or onto plastic wrap laid out on a baking sheet. Immediately cover the top of the pastry cream with plastic wrap and allow it to cool to room temperature. Refrigerate overnight.