Heat olive oil in a large skillet over medium-high heat. Add the lean ground beef and cook until browned, about 7-10 minutes.
Mix in the tomato paste, minced garlic, dried oregano, dried basil, dried thyme, salt, and pepper. Let the flavors blend for 1-2 minutes.
Transfer the beef mixture to a 6- to 8-quart Crock-Pot. Add diced celery, diced carrots, kidney beans, cannellini beans, tomato sauce, diced tomatoes, broth, and red pepper flakes if using.
Taste the soup and adjust seasonings if needed. Garnish with fresh parsley and Parmesan cheese if using.