Brown the beef and onion. Set a deep skillet over medium-high heat. Add the ground beef and diced onion, breaking the meat into small crumbles as it cooks. Brown everything until the beef loses its pink color and the onion softens. Drain excess fat if needed so the sauce does not turn greasy.
Add the garlic, pasta, tomatoes, and broth. Stir in the garlic first and let it cook for about 30 seconds, just until it smells fragrant. Then add the pasta, tomato sauce, diced tomatoes, broth, and oregano. Push the pasta down so it sits under the liquid as much as possible.
Simmer until the pasta is tender. Bring the pan to a gentle boil, cover it loosely, and simmer 12 to 15 minutes, stirring twice. Stirring keeps the pasta from sticking to the bottom and helps it cook evenly. If the sauce looks too thick before the pasta is done, add a splash of broth or water.
Fold in the mozzarella. When the pasta is tender, turn off the heat and fold in the mozzarella. The leftover heat melts it into the sauce and gives the dish a creamy, stretchy finish. Let the pan sit for two minutes before serving so the sauce thickens a little.
