Heat oil in saucepan set over medium-high heat; cook ground beef, salt and pepper for 5 to 8 minutes or until slightly browned.
Add onion, jalapeños, green olives, capers, garlic, chili powder, cumin and oregano; cook for 3 to 5 minutes or until vegetables are slightly softened.
Add rice, broth and tomatoes; bring to boil. Cover and reduce heat to low; cook for 15 to 20 minutes or until rice is tender and most of the liquid is absorbed. Let stand for 5 minutes. Fluff with fork. Transfer to large bowl; let cool completely. Stir in cheese and cilantro; refrigerate until ready to use.
Brush edges of each wrapper with cold water. Place heaping 1/4 cup filling in center of each square; bring edges of each square together to create triangle shape and enclose filling. Crimp edges to seal.
Preheat air fryer according to manufacturer’s instructions.
Place 4 empanadas in air fryer basket. Drizzle with 1 tbsp oil. Air fry at 400°F, turning empanadas halfway through, for 10 to 15 minutes or until golden brown and filling is heated through. Repeat with remaining empanadas.
Serve empanadas with sour cream for dipping.
Substitute ready-cut empanada pastry, wonton wrappers or potsticker wrappers for egg roll wrappers if desired.