Heat a large pot or Dutch oven over medium-high heat with the olive oil. Once hot, add the ground beef and brown for 3-4 minutes before breaking apart and added the diced onion. Cook both together until the beef is cooked through, another 3-4 minutes.
Add the tomato paste, garlic, salt, and pepper. Stir everything together and cook for 1-2 minutes until the garlic is fragrant.
Stir in the crushed tomatoes, beef broth, and Worceshtershire sauce. Bring to a simmer, cover, and cook for 15 minutes.
Add the diced potatoes and frozen mixed vegetables and stir everything together. Cover and cook for an additional 15 minutes. (You can let the soup simmer for longer to further develop flavors.)
Stir in the balsamic vinegar and hot sauce. Salt to taste before serving with grilled bread, cornbread, or crackers.