Prepare the Dough: In a large mixing bowl, whisk together the gluten-free flour and salt. Cut in the cold unsalted butter until the mixture resembles coarse crumbs. Beat the egg and mix with cold water; add gradually to the flour mixture until a dough forms. Wrap in plastic wrap and chill for about 30 minutes.

Make the Filling: Sauté the onions and bell peppers in a skillet until tender, about 5 minutes. Stir in the chicken and cumin, heating through and adding the cheese until melted. Let the filling cool.

Roll Out the Dough: Lightly flour a clean surface and divide the dough into portions. Roll each to about 1/8 inch thick and cut into circles, approximately 4-5 inches in diameter.

Assemble the Empanadas: Place a generous spoonful of filling on one half of a dough circle. Fold over to create a semi-circle and seal by pressing edges together. Crimp with a fork.

Egg Wash and Bake/Fry: Preheat oven to 375°F (190°C) for baking. Brush each empanada with egg wash. Bake for 20-25 minutes until golden, or fry in hot oil for 3-4 minutes per side until crispy.

Cool and Serve: Place baked or fried empanadas on a wire rack to cool slightly. Serve warm with dipping sauces or toppings.