Heat a large pot over medium heat. Add the ground beef and cook until browned, breaking it up with a spoon as it cooks.
Add the diced onion and minced garlic to the pot. Cook for 3 to 4 minutes until the onion softens.
Pour in the crushed tomatoes and beef broth. Stir in the dried oregano, salt, and black pepper.
Add the penne pasta and stir so it is mostly submerged in the liquid. Bring the mixture to a boil.
Reduce the heat to low, cover the pot, and simmer for 15 to 18 minutes. Stir once or twice during cooking to keep the pasta from sticking.
Remove the pot from the heat when the pasta is tender and most of the liquid has been absorbed. Stir in the grated Parmesan cheese before serving.