Preheat the oven to 350°F (175°C).
Cook the egg noodles according to package instructions until al dente. Drain and set aside.
In a large skillet, heat olive oil over medium heat.
Add diced onion and cook for 3-4 minutes until softened.
Add minced garlic and cook for 1 minute until fragrant.
Add ground beef to the skillet, breaking it apart with a spoon. Cook until browned and no longer pink, about 6-8 minutes. Drain excess fat if necessary.
Stir in diced tomatoes with their juice, tomato sauce, beef broth, dried oregano, dried basil, salt, and black pepper.
Bring the mixture to a simmer and cook for 10 minutes, stirring occasionally.
Remove the skillet from heat and stir in the cooked egg noodles until well combined.
Transfer the mixture to a 9×13-inch baking dish.
Sprinkle shredded cheddar and mozzarella cheeses evenly over the top.
Bake in the preheated oven for 20-25 minutes, or until the cheese is melted and bubbly.
Remove from the oven and let the casserole rest for 5 minutes before serving.