01 - Heat olive oil in a large skillet over medium heat. Sauté chopped onion until softened, about 3 minutes, then add minced garlic and cook for 30 seconds.
02 - Add ground beef to the skillet, breaking it up with a spatula. Cook until browned and fully cooked, approximately 5 to 6 minutes. Drain excess fat if necessary.
03 - Incorporate ground cumin, chili powder, smoked paprika, salt, and black pepper. Cook for 1 to 2 minutes until aromatic, then remove from heat.
04 - Combine refried beans, lime juice, and chopped cilantro in a small bowl, mixing thoroughly.
05 - On a workspace, lay out each tortilla. Spread 2 tablespoons of the bean mixture over half of each tortilla, add a portion of the beef filling, then evenly sprinkle both cheeses over the fillings.
06 - Fold each tortilla in half to encase the fillings securely.
07 - Preheat a large nonstick skillet or griddle over medium heat. Lightly brush the exterior of each quesadilla with softened butter.
08 - Cook in batches for 2 to 3 minutes per side until the tortillas are golden brown and the cheese has melted. Remove and allow to rest for 1 minute before slicing.
09 - Serve warm with optional accompaniments such as salsa, sour cream, sliced jalapeños, and fresh cilantro.