In a large mixing bowl, combine the gluten-free all-purpose flour and salt. Cut in the cold cubed unsalted butter until the mixture resembles coarse crumbs. Beat the egg in a separate bowl, then mix it into the flour mixture, adding cold water until a cohesive dough forms. Wrap in plastic wrap and refrigerate for 30 minutes.

Heat a skillet over medium heat, add oil, and sauté chopped onions and bell peppers for 4-5 minutes. Stir in shredded chicken and cumin, cooking for 2 more minutes, then mix in cheese until melted. Cool slightly.

Preheat oven to 375°F and line a baking sheet with parchment paper. Roll out the chilled dough to 1/8 inch thick. Use a round cutter to cut circles, then place filling on one half of each circle and fold to seal.

Transfer empanadas to the baking sheet. Beat an egg for egg wash and brush it over the empanadas. Bake for 20-25 minutes until golden brown.