Combine beef, diced onion, and garlic in a large skillet; cook and stir until beef is no longer pink, 5 to 8 minutes. Season with salt.
Transfer beef to a saucepan over low heat. Add 3/4 cup Cheddar cheese, mozzarella cheese, and milk. Cook and stir until cheese is melted, 3 to 5 minutes.
Melt half the butter in a large skillet over medium heat. Cook 1 tortilla until golden brown on the bottom, about 3 minutes. Flip tortilla and spread with 1 tablespoon dressing. Spoon half of the beef mixture over the tortilla; fold in half. Cook until tortilla is golden brown, 1 to 2 minutes per side. Transfer to a serving plate. Repeat with second tortilla.
Sprinkle remaining 1/4 cup Cheddar cheese over tortillas. Let cool, about 5 minutes. Cut into wedges and serve with lettuce, tomato, and sliced onion.
