Brown the beef. Heat a drizzle of avocado oil in a deep pan over medium-high heat. Add the ground beef and cook until fully browned. Transfer the cooked beef to a plate and set aside.
Sauté the vegetables. In the same pan, add a little more avocado oil if needed. Add the shallots, carrot, and celery. Sauté for about 5–7 minutes, until softened and fragrant.
Add garlic and beef. Stir in the minced garlic and return the cooked ground beef to the pan. Mix well and cook for another minute to combine flavors.
Build the sauce. Add the Italian seasoning, diced tomatoes, tomato paste, balsamic vinegar, and sugar (if using). Pour in the beef stock and stir until everything is well combined. Bring to a boil, then reduce the heat to low, cover, and simmer for about 20 minutes, stirring occasionally, until the sauce is thick and rich.
Cook the gnocchi. Add the gnocchi directly into the sauce and stir to coat. Cover and simmer for about 3 minutes, or according to package directions, until the gnocchi is tender. Stir occasionally to prevent sticking, and add a splash more stock if the sauce becomes too thick.
Add cheese and broil. Taste the sauce and season with salt and black pepper as needed. Transfer everything to a baking dish (or keep it in the same pan if oven-safe). Top generously with the grated cheddar and place under the broiler for 3–5 minutes, until the cheese is melted, golden, and bubbly.
Finish and serve. Serve immediately and enjoy that melty, saucy perfection.