Whisk together milk, yeast, and sugar in a large bowl. Cover and let stand until mixture is foamy, about 10 minutes.

Sift flour into milk mixture. Add oil and salt, stirring with a rubber spatula until a shaggy dough forms. Knead dough until smooth and soft, about 5 minutes.

Shape dough into a ball. Brush lightly with oil, cover and let rise in a warm place until doubled, about 90 minutes.

Stir together mozzarella and ricotta. Season with pinch of salt and set aside.

Divide dough into 4 portions. Roll into ovals, spread cheese mixture, fold edges inward, and seal. Create slits and rolled borders on dough.

Spread remaining cheese mixture onto flatbreads and let rest in a warm place until puffed, about 30 minutes.

Preheat oven to 400°F (200°C). Bake until edges are golden, about 20 minutes.

Make a well in the center of each bread, add egg yolk, and bake until yolks are thickened but still runny, about 40 seconds.