In a large mixing bowl, combine gluten-free all-purpose flour and salt. Cut in cold, cubed unsalted butter until the mixture resembles coarse crumbs. Gradually mix in the egg and enough cold water to form a soft dough ball. Wrap in plastic wrap and chill for 30 minutes.

In a sauté pan over medium heat, add a splash of oil and cook finely chopped onions and diced bell peppers until tender, about 5-7 minutes. Stir in shredded chicken and cumin, mixing well until heated. Add cheese, stirring until melted, then remove from heat.

Preheat the oven to 375°F (190°C) and line a baking sheet with parchment paper. On a floured surface, roll out the chilled dough to about 1/8 inch thick. Cut circles about 4-5 inches in diameter. Place filling on one half, fold the other half over, and press edges to seal.

Transfer filled empanadas to baking sheet. Beat an egg and brush the surface of each empanada. Bake for 20-25 minutes until golden brown. For a crispy texture, fry until browned on both sides.