Start by heating a large Dutch oven over medium-high heat. Add the lean ground beef, breaking it apart with a spoon. Cook until it's mostly browned, with only a small amount of pink remaining. This process should take about 5 minutes.

Once the beef is nearly cooked through, add the chopped onion to the pot. Continue cooking for an additional 5 minutes, or until the onion is soft and the beef is fully browned. Season this mixture with a pinch of salt and pepper to taste.

Stir in the minced garlic, tomato paste, and dried Italian seasoning, cooking for another minute.

Next, pour the beef broth into the pot, and use your spoon to scrape any browned bits off the bottom of the pan. These brown bits are packed with flavor and will enhance the overall taste of your soup. Then add the diced tomatoes and potatoes, stirring to incorporate everything evenly. Allow the mixture to come to a boil, then reduce the heat and simmer for 5-7 minutes, or until the potatoes are almost fork-tender.

Add the bag of frozen mixed vegetables to the pot. Continue to cook for about 5 minutes, until the vegetables are heated through and the potatoes are fully tender. Taste your soup and adjust the seasoning with additional salt and pepper as needed.

Shaved Parmesan cheese sprinkled on top makes a delightful garnish, adding a touch of richness to the dish. Serve the homemade vegetable beef soup hot, with a side of crusty bread or crackers for dipping.