In a large skillet over medium-high heat, brown the ground beef until cooked through, then drain the excess fat.
Add the cooked beef to a 6-quart slow cooker.
Incorporate the onion, carrots, celery, minced garlic, diced tomatoes, tomato sauce, beef broth, kidney beans, and cannellini beans.
Stir in the oregano, basil, thyme, salt, and black pepper.
Cover and cook on low for 6 to 8 hours or on high for 3 to 4 hours.
Thirty minutes before serving, cook the ditalini pasta in a separate pot of boiling salted water according to package instructions until al dente.
Drain the pasta and stir it into the soup just before serving to prevent the pasta from over-absorbing the broth.