Add the beef and onions to a Dutch oven or large pot with oil. Heat over medium-high heat. Cook, breaking up the beef into very small pieces, until the beef is browned and the onions are tender (about 6 minutes). Stir in the garlic, oregano, and basil and cook about 1 minute. Season with salt and pepper. Stir in the tomato paste until well incorporated
Add the diced tomatoes, tomato sauce, and sweetener. Bring to a low boil, then reduce to a simmer. Simmer the sauce for at least 30 minutes and up to 1 hour, stirring occasionally, until sauce is thickened to your liking. Add the balsamic vinegar if desired. Stir to combine. Serve over pasta or veggies of choice!