Add olive oil to dutch oven and heat over medium heat. Once oil is warmed, add onions, garlic, and carrots to the pot and cook until softened, about 10 minutes.
Next, add ground beef, season with salt and pepper to taste, break up with wooden spoon, and cook until meat has browned.
Once the beef is cooked through, add the garlic. Add the red wine vinegar and cook until the vinegar has dissolved. Add the tomato paste and cook until combined.
Next, add the beef broth and cook until it has reduced into the sauce, stirring frequently, about 15 minutes.
Lastly, add the diced tomatoes and summer the sauce on low for at 45 minutes to an hour.
