In large skillet over medium-high heat, melt butter. Add ground beef and cook until browned, approximately 5 to 6 minutes. Remove ground beef from skillet and drain fat.
Add garlic, onion, and bell pepper to skillet. Cook until fragrant, 1 to 2 minutes.
Add in cumin, paprika, salt, pepper, and chili powder. Cook an additional 1 to 2 minutes, stirring frequently.
Pour in beef broth, then return ground beef to skillet. Simmer approximately 10 minutes or until liquid has evaporated.
Transfer mixture to bowl and let cool.
In separate small bowl, mix egg and water together until combined.
Lay empanada discs on flat surface. Work in batches if needed.
Form Empanadas: Place approximately 3 tablespoons of filling mixture in center of each empanada disc. Fold dough in half, bringing one edge over dough filling to meet other edge. Pinch edges with fingers or press with tines of fork to seal. Lightly brush egg wash on outside of dough. Repeat until all empanadas are formed.
Preheat air fryer to 330° Fahrenheit.
Spray air fryer basket with air-fryer-safe cooking spray. Place empanadas in basket in one even layer, not touching or overlapping. Work in batches as needed.
Cook empanadas at 330° Fahrenheit for 8 to 9 minutes, until golden brown and warmed through. Repeat until all empanadas are cooked. Serve hot.