In a large bowl, combine the beef, egg, garlic, salt, pepper, basil, and arrowroot flour. Mix until well combined.
Heat the oil in a large pot or dutch oven over medium heat. When the oil is hot, add the meatballs in a single layer (you may need to do it in two batches) and cook until golden brown on both sides, 2 to 3 minutes per side. (They don’t need to be cooked through, just browned as they will continue to cook later.) Transfer the browned meatballs to a plate and set aside.
In the same pot, add the onion, garlic, and a pinch of salt and pepper and cook, stirring, until the onions are tender, about 4 minutes. Add the tomato bone broth soup, chicken broth, balsamic, and Italian seasoning and stir to combine. Add the meatballs back into the mixture and any of it’s juices.
Add the pasta and gently stir to combine, bring to a boil. Once boiling, reduce the heat to a light simmer and cook, uncovered and gently stirring often, until the pasta is tender and sauce has thickened, 12 to 15 minutes.
Taste and sauce and add salt and pepper, if desired. Serve topped with basil!