Heat the oven to 375°F and place a rack in the center.
Warm olive oil and butter in a 10-inch oven-safe skillet over medium heat.
Brown the sausage, breaking it up with a spoon, until no longer pink. Spoon off excess fat.
Stir in onion and cook until translucent, 3–4 minutes. Add garlic and cook 30 seconds.
Fold in spinach and cook until wilted. Spread the mixture in an even layer.
Whisk eggs with milk, salt, pepper, and red pepper flakes. Stir in half the cheddar.
Pour the egg mixture over the skillet fillings. Gently stir, then top with remaining cheddar and Parmesan.
Cook without stirring until the edges just begin to set, about 2 minutes.
Bake until the center is barely set and the top is lightly golden, 10–12 minutes. Rest 5 minutes before slicing.