Brown the beef with the onion in a large skillet over medium-high heat, breaking it up, 6–7 minutes. Drain excess fat.
Stir in garlic, chili powder, cumin, paprika, oregano, salt, and pepper. Cook until fragrant, about 1 minute.
Add tomato sauce, green chiles, and broth. Simmer, stirring, until thick and saucy, 5–7 minutes.
Off heat, fold in refried beans, cilantro, and lime juice. Let the filling cool 5 minutes.
Warm the tortillas under a damp towel in the microwave until pliable, 30–45 seconds.
Spoon filling across the lower third of each tortilla. Top with cheese. Fold sides in and roll tightly, seam down.
Heat the oil in a deep skillet to about 350°F over medium-high heat.
Fry chimichangas seam-side down until deep golden, 2–3 minutes per side. Drain on a rack or paper towels.
Serve hot with salsa and sour cream.