Heat a large pot over medium-high heat. Add the ground beef and cook, breaking up with a spoon, until browned and no pink remains, about 6–8 minutes. Drain excess fat if necessary.
Add olive oil if needed and sauté the diced onion until translucent, 4–5 minutes. Add minced garlic and cook 1 minute. Stir in tomato paste now if using and cook 30 seconds.
Add carrots, celery, and potatoes to the pot. Pour in broth and diced tomatoes with their juices. Add thyme and bay leaf. Bring to a boil, then reduce heat and simmer 15–20 minutes until vegetables are tender.
Stir in green beans and corn and simmer 6–8 minutes more. Add kale or spinach in the last 2–3 minutes to wilt. Season with salt and pepper to taste.
Remove bay leaf, ladle soup into bowls, and garnish with parsley or Parmesan. Serve hot with crusty bread.
Notes
To thicken the soup without cream, mash a cup of the cooked potatoes against the pot and stir.
This soup freezes well; cool completely before transferring to freezer-safe containers.
Use frozen mixed vegetables to save time and reduce prep.