Heat olive oil in a large nonstick skillet over medium-high heat. Add onion, pepper, and garlic, and cook, stirring constantly, 4 minutes or until tender. Stir in beef and next 4 ingredients; cook, stirring often, 8 minutes or until beef is cooked through. Stir in tomatoes and next 3 ingredients; cook 10 to 15 minutes or until mixture thickens.
Spread about 1 heaping tablespoon beef mixture evenly in center of empanada disks. Brush edges of dough with water. Fold dough over filling, pressing edges with a fork to seal. Place on baking sheet.
Pour oil to a depth of 1 inch into a soup pot or Dutch oven; heat to 350° to 360°. Fry empanadas, in batches, 1 to 2 minutes on each side or until golden. Drain on paper towels. Serve with Avocado Salsa Verde.
For a lighter variation, skip the frying step: Brush both sides of the empanadas with oil, and bake on a lightly greased baking sheet at 400° for 15 minutes.