In the bowl of a stand mixer fitted with the paddle attachment, combine 1 cup (125 grams) of flour, ¼ cup (50 grams) of granulated sugar, the yeast, and kosher salt. Beat on low speed until everything is well mixed.
Add the warm milk to the mixture. Beat just until combined; this should take only a few moments.
Add 2 eggs (100 grams) and the egg yolk. Beat at medium-low speed until combined, which should take about a minute.
With the mixer on low speed, gradually add the remaining 1½ cups (188 grams) of flour, mixing just until combined.
Switch to the dough hook attachment. Beat on low speed until the dough becomes relatively smooth and elastic, about 6 to 9 minutes.
Add the softened butter, one tablespoon (14 grams) at a time. Beat until incorporated after each addition.
Increase the mixer speed to medium-low and continue to beat until a smooth, elastic dough forms, for an additional 6 to 9 minutes.
Turn the dough out onto a clean surface, knead it gently 4 to 5 times to form it into a smooth round.
Spray a large bowl with cooking spray, then place the dough inside, turning to grease the top. Cover and let rise until doubled in size.
Once risen, punch down the dough gently, then cover and let it rest for 10 minutes.
Turn the dough out onto a clean surface. Divide into 12 portions, each about 52 grams.
Press or roll each dough ball into a 3½-inch round and place on prepared pans.
Cover and let rise again until puffed, about 30 to 40 minutes.
Preheat your oven to 350°F (180°C). Meanwhile, stir together strawberries, lemon juice, and remaining 2 teaspoons of granulated sugar.
Using a ¼-cup glass jar or dry measuring cup, make a well in the center of each dough round.
Divide the Lemon Pastry Cream among the rounds, spreading it to fill the well.
Brush the dough with the egg wash and sprinkle with pearl sugar.
Bake until light golden brown, about 8 to 10 minutes.