Melt 2 tablespoons butter in a large saucepan over medium-high heat. Add the garlic and onion and cook until soft, 3 to 4 minutes. Add the tomato paste and cook for 2 minutes more. Add the remaining butter, olive oil, tomato purée, 2 teaspoons salt, sugar, pepper, Italian seasoning, fennel seeds, and wine, and simmer until thick, about 5 minutes.
Meanwhile, make the meatballs. Mix the remaining 2 teaspoons of salt with the ground beef. Use a ½ tsp to roll the meat into tiny balls. Place meatballs into sauce and reduce the heat to medium. Cook until the meatballs are cooked through, 6 to 8 minutes.