In a large skillet over medium-high heat, cook ground beef, onion, and carrots until beef is browned and carrots start to soften. Drain excess fat if needed.
Add garlic, salt, pepper, Italian seasoning, and paprika. Cook 30 seconds.
Stir in squash puree and drained tomatoes. Add broth and bring to a gentle boil.
Stir in dry pasta. Reduce heat to medium-low, cover, and simmer 10–12 minutes, stirring occasionally, until pasta is tender and sauce is thick and creamy.(Add small splashes of broth or water if needed.)
Stir in milk or cream, peas, and cheese. Cook uncovered 2–3 minutes until peas are heated and sauce is silky.
Add more salt, pepper, or cheese as needed.