Preheat your oven to 375°F (190°C) and line a baking sheet with parchment paper.
In a large skillet, heat the olive oil over medium heat. Add the onion and garlic and sauté for 2-3 minutes or until the onion becomes translucent.
Add the red and green bell peppers and cook for an additional 3-4 minutes until softened.
Stir in the ground chicken and cook until it is browned and fully cooked through, about 5-7 minutes.
Add cumin, smoked paprika, chili powder, cayenne pepper, salt, and pepper to the skillet. Stir to combine the spices evenly with the chicken mixture.
Pour the tomato sauce into the skillet and stir well. Allow the mixture to simmer for 5 minutes, reducing any excess liquid.
Remove from heat and stir in fresh cilantro and shredded cheddar cheese until the cheese is melted and well combined. Allow the filling to cool slightly.
Roll out the pie dough and cut out circles, about 4 inches in diameter, using a biscuit cutter or the rim of a glass.
Place a heaping tablespoon of the chicken mixture onto one half of each dough circle, leaving space around the edges.
Fold the dough over the filling to form a half-moon shape, pressing the edges together with a fork to seal. Repeat with the remaining dough and filling.
Brush the top of each empanada with the beaten egg.
Transfer the empanadas to the prepared baking sheet and bake in the preheated oven for 20-25 minutes, or until golden brown.
Remove from the oven and allow to cool slightly before serving.