Bring a large pot of salted water to a boil. Cook the gnocchi according to the package directions. Once the gnocchi float to the surface and are tender, drain well and set aside.
While the gnocchi cook, add the ground beef, chopped onion, and diced carrots to a large skillet over medium-high heat. Cook for 8–10 minutes, breaking the beef into crumbles, until the beef is fully browned and the onion and carrots have softened. Drain any excess grease from the skillet.
Add the frozen peas, ketchup, water or beef broth, Worcestershire sauce, garlic powder, Italian seasoning, salt, and black pepper. Stir until evenly combined. Reduce the heat to medium and cook for 3–5 minutes, stirring occasionally, until the peas are heated through and the sauce coats the beef and vegetables.
Add the drained gnocchi to the skillet. Gently stir until the gnocchi are evenly coated in the beef and vegetable mixture.
Cook for an additional 1–2 minutes, stirring gently, until everything is hot and well combined. Serve immediately and enjoy!