01 - Preheat oven to 375°F. Lightly grease a 9x13-inch baking dish.
02 - Heat olive oil in a large skillet over medium heat. Add onion and cook 2–3 minutes until softened. Add garlic and cook 30 seconds more.
03 - Add ground beef to the skillet. Cook, breaking up meat, until browned and cooked through, about 5–6 minutes. Drain excess fat.
04 - Stir in green chilies, cumin, chili powder, smoked paprika, salt, and black pepper. Cook 1 minute. Remove from heat.
05 - Spread 1/2 cup enchilada sauce over the bottom of the prepared baking dish.
06 - Layer 4 tortillas over the sauce, overlapping slightly. Top with half of the beef mixture, 3/4 cup cheddar, and 1/2 cup Monterey Jack cheese.
07 - Drizzle 3/4 cup enchilada sauce over the layer. Repeat with remaining tortillas, beef, and cheese.
08 - Pour remaining enchilada sauce over the top. Sprinkle with any remaining cheese and black olives.
09 - Cover with foil and bake for 20 minutes.
10 - Uncover and bake an additional 10–15 minutes, until cheese is bubbly and lightly golden.
11 - Let stand 10 minutes before serving. Garnish with chopped cilantro and serve with sour cream if desired.