Bring a large pot of water to a boil. Cook pasta until just tender, 8 to 10 minutes or according to package directions. Drain.
Meanwhile, heat oil in a large skillet over medium heat. Add onion, carrot and celery and cook, stirring occasionally, until the onion is beginning to brown, 5 to 8 minutes.
Stir in garlic and Italian seasoning; cook until fragrant, about 30 seconds. Add beef and cook, stirring and breaking up with a spoon, until no longer pink, 3 to 5 minutes. Increase heat to high.
Stir in tomatoes and cook until thickened, 4 to 6 minutes. Stir in parsley and salt. Serve the sauce over the pasta, sprinkled with cheese.
Make Ahead Tip: Cover and refrigerate for up to 3 days or freeze in an airtight container for up to 3 months.