Preheat your oven to 375°F (190°C). Grease a 9x13-inch baking dish with cooking spray or oil.
In a large skillet, cook the ground beef over medium heat until browned and cooked through, breaking it apart with a spoon as it cooks.
Add the diced onion and minced garlic to the skillet with the ground beef, and cook for an additional 2-3 minutes until the onion is softened and translucent.
Season the beef mixture with Italian seasoning, paprika, salt, and black pepper to taste. Stir well to combine.
In the meantime, cook the pasta according to the package instructions in a large pot of salted boiling water until al dente. Drain the cooked pasta and set aside.
In a large mixing bowl, combine the cooked ground beef mixture, cooked pasta, diced tomatoes, tomato sauce, shredded cheddar cheese, shredded mozzarella cheese, and frozen mixed vegetables. Mix until all ingredients are well combined.
Transfer the mixture to the greased baking dish, spreading it out evenly.
Cover the baking dish with aluminum foil and bake in the preheated oven for 25-30 minutes.
After 25-30 minutes, remove the foil and continue baking for an additional 10-15 minutes, or until the casserole is hot and bubbly and the cheese is melted and golden brown on top.
Remove from the oven and let the Hamburger Supreme Casserole cool slightly before serving.