Combine the garlic, onions, salt and 5 cups water in a 12-inch high-sided saucepan and bring to a boil. Add the chicken breasts and bay leaf, and lower the heat to a simmer. Cook the chicken, partially covered, until cooked through, about 35 minutes. (To check for doneness, slit the chicken in half to make sure the interior is no longer pink.) Remove the chicken (reserve the broth) and allow to cool slightly. When cool enough to handle, shred by hand and place in a medium bowl.
Remove enough broth to leave about 2 cups in the pan with the onions and garlic (cool and refrigerate or freeze the extra broth for another use). Remove the bay leaf. Add the tomatillos and jalapenos and cook until the tomatillos are olive green, 10 to 12 minutes. With a slotted spoon, transfer the solid ingredients (onions, tomatillos and garlic) to a blender. Add the cilantro and process until smooth (using some of the liquid in the pan if needed). Season with salt and pepper. Pour the salsa back into the saucepan and bring to a boil; add the chicken and cook until the flavors incorporate, about 5 minutes. Adjust the seasoning. Remove from the heat and set aside to cool.
Preheat the oven to 400 degrees F.
To assemble the empanadas: Dust a flat surface with flour. Roll out the pizza dough about 1/8 to 1/4 inch thick. Using a 6-inch round cookie cutter (or a bowl or plate with the same diameter), cut the dough into circles. Expect to get about 3 circles from 1 pound of dough. Brush the egg wash over the surface of one dough round. Add 2 tablespoons of filling onto half of the circle and sprinkle about 1 ounce of mozzarella on top of the filling, if using. Fold the plain half over the filling. Seal the edges with fork tines or crimp decoratively. Repeat for the remaining empanadas. (Save any leftover filling in an airtight container in the fridge for up to a week for another use.)
Transfer the empanadas to a baking sheet lined with parchment paper. Using a pastry brush, brush the tops of the empanadas with the egg wash. Bake until crisp and golden brown, about 20 minutes. Let cool for about 10 minutes before serving.