Preheat the oven to 350°F (175°C). Lightly grease a 9×13-inch baking dish.
In a large skillet over medium heat, cook the ground beef, diced onion, and diced green bell pepper until the beef is browned and vegetables are softened, about 7-8 minutes.
Add the minced garlic, salt, black pepper, and smoked paprika to the skillet. Stir and cook for an additional 1-2 minutes until fragrant. Remove from heat and set aside.
In a large mixing bowl, whisk together the eggs and whole milk until fully combined.
Add the cooked ground beef mixture to the egg mixture and stir to combine.
Pour half of the egg and beef mixture into the prepared baking dish.
Sprinkle half of the shredded cheddar and mozzarella cheese evenly over the mixture.
Pour the remaining egg and beef mixture over the cheese layer.
Top with the remaining shredded cheddar and mozzarella cheese.
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 the casserole rest for 5 minutes before slicing.
Garnish with chopped fresh parsley before serving.