In a large skillet or saucepan over medium-high heat, brown the beef. Break it up into small bits as you cook. Once browned, transfer the beef and any juices to a clean bowl and set aside.In the same pan over medium-high heat, warm a teaspoon of olive oil. Add the onions, celery, and carrots, and cook until the onions are translucent and the carrots look softened, about five minutes. Add mushrooms and cook until the mushrooms are soft and tender, about 5 minutes. Add the garlic and stir until fragrant, about thirty seconds.Return the ground beef to the pan. Stir in the tomato sauce, ketchup, 1 tablespoon cider vinegar, Worcestershire sauce, sugar (if using), salt, and black pepper. Cover and simmer for 15 minutes.Taste the sauce, adding more vinegar, salt, or sugar if desired. If the sauce is too thin for your taste, simmer uncovered for another 5 to 10 minutes until the desired thickness is reached. (If you have time, you can continue simmering for up to an hour or more! The meat will just continue becoming more tender. Add extra liquid to the pan if the sauce starts to dry out.)
Serve on hamburger buns. Don’t forget a napkin.