Heat the olive oil in a large pot over medium-high heat. Add in the onion, celery, and carrots and sauté until they're tender. Add in the ground beef and use a wooden spoon or spatula to crumble it. Season with the Italian seasoning, red pepper flakes, salt and pepper. When the beef is cooked, stir in the garlic and cook for another minute.
Stir the tomato paste in with the vegetables. Add in the potatoes, diced tomatoes, parmesan cheese rind if using one, and beef broth. Stir together and scrape up any brown bits stuck to the bottom of the pot.
Bring the soup to a boil then reduce the heat to medium-low and let it simmer for about 25 minutes or until the potatoes are tender. Stir in the peas. Serve the soup garnished with chopped flat leaf parsley if desired.
