In a large skillet, heat oil over medium-low. Add onion, carrot, and garlic; season with salt and pepper. Cook, stirring often, until onion and carrot are tender, about 10 minutes.
Add beef, stirring to combine. Add broth, and simmer until meat is almost falling apart and liquid is reduced by half, about 10 minutes.
Meanwhile, in a large pot of boiling salted water, cook pasta until al dente according to package directions. Drain; transfer to a large bowl. Add
sauce and Parmesan, and toss well. Divide among serving bowls; top with more cheese, if desired.
You can make the sauce ahead of time and keep it covered in the refrigerator. Gently reheat the sauce on the stove while the pasta is cooking.