Place flour into a large bowl and make a well in the center. Crack eggs into the well; gently beat eggs with a fork until blended, then use the fork to gradually draw flour in from the sides. Mix until all flour is incorporated.

Turn dough out onto a lightly floured surface; knead until smooth and elastic (3 to 4 minutes). Cover with plastic wrap and let rest for at least 20 minutes.

Mix ricotta, mozzarella, and Parmesan together in a bowl for the filling. Whisk water and egg together in another bowl for egg wash.

Bring a large pot of salted water to a boil.

Roll dough into a thin sheet; cut with a heart-shaped cookie cutter. Brush the edges of each heart with the egg wash. Spoon filling into the center of half of the hearts. Place remaining hearts, egg wash-side down, over filling; press edges together to seal.