Preheat oven to 400°F (200°C) and line a large baking sheet with parchment paper.
In a medium bowl, combine the shredded mozzarella, Monterey Jack, oregano, and garlic powder until evenly distributed.
Place one dough disc on a clean, flat surface and spoon approximately 3 tablespoons of the cheese mixture onto the center.
Fold the dough over the filling to create a half-moon shape, pressing the edges together firmly to seal.
Use the tines of a fork to crimp the edges of the dough, ensuring a complete seal to prevent leakage during baking.
Arrange the assembled empanadas on the prepared baking sheet, spaced at least 1 inch apart.
In a small bowl, whisk the egg and water to create an egg wash.
Lightly brush the top of each empanada with the egg wash and sprinkle with sea salt.
Bake for 20 to 25 minutes until the pastry is puffed and deep golden brown.
Remove from the oven and rest for 5 minutes to allow the cheese to set slightly before serving.