In the bowl of a food processor, add the flour, salt, and baking powder. Pulse a few times just to combine. Add the cold butter and pulse until the mixture resembles a coarse meal. Add the yogurt and pulse again until the dough comes together.

Turn the dough out onto a floured work surface. Knead the dough with the heels of your hands a few times to smooth it out.

Pat the dough into a log shape and roll this into an 8 x 10-inch rectangle. Dust both sides of the dough with flour. Fold it in three like you would a letter. Roll it again into an 8 x 10-inch rectangle and fold in three.

Wrap the dough in plastic and chill in the refrigerator for at least 30 minutes.

Preheat your oven to 375°F. Line 2 baking sheets with parchment paper.

In a mixing bowl, combine the ricotta, mozzarella, and parmesan cheese. Break or crumble the bacon onto the cheese. Add the basil. Using a spatula or wooden spoon, fold the bacon and basil into the cheese mixture.

Remove the eggs from the refrigerator and allow them to come to room temperature.

Cut the dough into 4 equal pieces and form them into circles. On a lightly floured work surface, roll each piece out to a circle that is approximately 1/4 to 1/2-inch thick. Transfer the dough circles to the parchment-lined baking sheets.

Spread 1/4 of the cheese filling on each pastry, leaving 1 to 1-1/2 inches free around the perimeter. Fold the edges of the dough over the cheese, pleating each fold over the previous one so the dough forms a rustic lip that holds the filling in place.

Whisk one egg in a small bowl and brush the edges of each galette.

Place the pans in the oven and bake the galettes for 25 minutes or until the pastry is just turning golden brown.

Crack an egg on top of each galette. Return to the oven and bake again for an additional 15 minutes, or until the egg whites are opaque and set and the yolks are still a little runny.