Brown the ground beef in a large pot over medium heat, breaking it up as it cooks. Add the onion and garlic once the beef is mostly cooked and continue until the onion softens.
Stir in the carrots, celery, and green beans. Cook for two minutes to let the vegetables start to warm.
Add the diced tomatoes with their juice, cannellini beans, beef broth, and Italian seasoning. Season with salt and pepper.
Bring the mixture to a simmer, then reduce the heat and cook for 20 minutes until the carrots and green beans are tender.
Remove the pot from the heat and let the stew cool completely. Divide into freezer-safe containers or bags, leaving a little room for expansion.
Label and freeze. To serve, thaw overnight in the refrigerator and reheat on the stove until hot. Top each bowl with grated Parmesan.