Step 1

Stir 1/4 cup warm water, 1 tablespoon granulated sugar, and 1 teaspoon active dry yeast together in a small bowl. Let sit until foamy, about 5 minutes. (If it does not foam, get fresh yeast and start over.) Meanwhile, stir 3 cups all-purpose flour and 1 teaspoon kosher salt together in a large bowl.

Step 2

Make a well in the flour mixture. Add the yeast mixture, 1 cup sour cream, 4 tablespoons melted unsalted butter, 1 large egg, and 1 tablespoon baking powder into the well. Stir until the dough begins to come together.

Step 3

Transfer onto a lightly floured surface and knead until smooth and elastic, 5 to 7 minutes. Coat the dough bowl with cooking spray. Place the dough in the bowl. Cover and let rest in a warm place until soft and pillowy, 30 to 45 minutes (it does not have to double). Meanwhile, make the cheese filling.

Step 4

Mix 1 pound shredded low-moisture mozzarella cheese, 8 ounces crumbled feta cheese, 1 large egg, and 1 tablespoon melted unsalted butter together in a large bowl with your hands until well-combined. Divide into 4 portions (about 7 ounces each) and shape each portion into a ball.

Step 5

Arrange 2 racks to divide the oven into thirds and heat the oven to 400°F. Line 2 baking sheets with parchment paper. Whisk 1 large egg yolk and 1 tablespoon milk together in a small bowl with a fork.

Step 6

Punch down the dough and divide it into 4 portions (about 7 ounces each). Roll out each portion into an 8-inch round.

Step 7

Place a cheese ball in the center of each round. Fold the edges of the dough over the filling so that it is completely enclosed, then pinch the edges together to seal.

Step 8

Flip the stuffed rounds over. Use the palm of your hand or a rolling pin to evenly flatten each one until 1/2-inch thick and about 6 inches wide. Transfer onto the baking sheets, 2 per sheet. Poke the tip of a knife into the middle of each one and use a finger to make a hole about 1/2-inch wide to let steam escape during baking. Brush all over with the egg yolk mixture.

Step 9

Bake, rotating the baking sheets between racks and from front to back halfway through, until golden-brown, 15 to 20 minutes total. Let cool for 10 minutes before slicing and serving.