Combine ½ cup warm milk with 1 tablespoon active dry yeast and 1 teaspoon granulated sugar. Let sit for 5 minutes or until the mixture is foamy.

Combine 3 ½ cups all-purpose flour with 1 teaspoon salt, and ¼ cup sugar in a bowl of a stand mixer. Add the yeast mixture along with 5 eggs. Mix the dough using the dough hook and knead for 8 minutes. Add the butter a few pieces at a time while the mixer is mixing on low. Continue to add all of the butter. Knead the dough for 4-5 minutes, scraping down the sides of the bowl as necessary. The dough will be very soft and shiny.

Transfer the dough to a clean bowl, cover with plastic wrap and let rise in a warm area for 1 hour.

Continue to proof the dough in the fridge overnight.

Remove the dough from the fridge and divide it into 12 equal portions. Roll each portion into a ball and place on two lined baking sheets, 6 per sheet. Loosely cover and let rise for 2 hours or until doubled in size.

Meanwhile, cook the bacon. Preheat oven to 350 degrees F. Line a baking sheet with aluminum foil. Place a wire rack on top and lay the bacon in one even layer. Bake the bacon until it's halfway cooked, about 15 minutes. The bacon should be lightly browned but not crispy. Remove from the oven and let cool.

Shape the brioche tarts. Using your hands, gently press into the center of each dough ball, pushing outward to create a cavity. The cavity should be big and deep enough to hold an egg. Line the cavity with a strip of bacon and crack an egg side the bacon wall.

Whisk together 1 egg yolk with 1 tablespoon heavy cream for the egg wash. Brush the edges of the tarts with the egg wash and sprinkle 2 tablespoon grated parmesan on top. Bake the tarts until the edges are golden brown, the bacon is crispy, and the egg white is completely opaque but still jiggly, about 18-20 minutes.

Let cool slightly and serve the bacon and egg brioche tarts warm.