Preheat your oven to 375°F (190°C) and grease a 9x13 inch baking dish.
In a large mixing bowl, combine the ground beef, breadcrumbs, eggs, mozzarella cheese, milk, onion, garlic, Italian seasoning, salt, pepper, and paprika. Mix well until fully combined.
Spread half of the meat mixture evenly in the bottom of the prepared baking dish.
Layer the diced bell peppers, zucchini, and carrots over the meat layer, spreading them evenly.
Spoon the marinara sauce over the vegetable layer, spreading it out to cover.
Top the marinara sauce with the remaining meat mixture, pressing it down gently to form an even layer.
Sprinkle the shredded cheddar cheese over the top of the casserole.
Cover the baking dish with aluminum foil and bake for 30 minutes.
After 30 minutes, remove the foil and bake for an additional 15 minutes, or until the cheese is bubbly and golden.
Allow to cool for 5-10 minutes, then garnish with chopped parsley before serving.