Heat a very large skillet (for this full recipe, it should be a deep 12-inch pan) over medium high heat and brown the beef, stirring until no pink remains, about 5 minutes. Drain the beef and set aside.
Wipe out the skillet, add the oil, and heat it over medium heat. Add the peppers, carrots, onion and garlic and sauté until almost tender, about 5 minutes.
Add the ground beef back to the skillet, as well as the basil, oregano, tomatoes with their juice, water, Worcestershire sauce, and chili powder if using. Season with salt and pepper, turn the heat to high, and bring to a simmer. Add the pasta, stir and cover. Lower the heat to medium and simmer covered, stirring occasionally, until the pasta is tender, and most of the liquid is absorbed, 8 to 10 minutes. Taste and season again if needed.
Sprinkle the cheese over the casserole then cover for just 1 more minute until the cheese is melty, and serve. Serve this right out of the pan.
In some parts of the country this is known as goulash or American Goulash. I did not even know this was a thing until I started researching American Goulash recipes, and realized that this recipe was (accidentally!) the very definition of that dish. American Goulash is a tomato based ground beef meal or sorts with the pasta baked right into the mix. There is usually peppers (check), elbow macaroni (check) and cheese (check) involved.