Preheat the oven to 350°F (175°C).
Heat olive oil in a large skillet over medium heat.
Add diced onion and green bell pepper to the skillet and sauté for 4-5 minutes until softened.
Add minced garlic and cook for an additional 1 minute until fragrant.
Add ground beef to the skillet and cook until browned, breaking it apart with a spatula, about 6-8 minutes.
Drain excess fat from the skillet and season the beef mixture with salt, black pepper, and paprika. Stir to combine and remove from heat.
In a large mixing bowl, whisk together eggs and whole milk until fully combined.
Add the cooked ground beef mixture to the egg mixture and stir to combine.
Grease a 9×13 inch baking dish with cooking spray or butter.
Pour the egg and beef mixture into the prepared baking dish.
Sprinkle shredded cheddar and mozzarella cheese evenly over the top.
Bake in the preheated oven for 40-45 minutes, or until the eggs are set and the top is golden brown.
Remove from oven and let cool for 5 minutes before slicing and serving.