Heat the 1 tablespoon of olive oil in a large skillet over medium-high heat. Drop in the ground beef and Italian sausage, cooking for 5 to 6 minutes while continuously breaking the meat apart into fine crumbles with a firm spoon until thoroughly browned and no pink remains.

Tilt the pan slightly to drain away any heavy excess grease, then stir in the minced garlic and cook for exactly 60 seconds until fragrant. Transfer the hot meat mixture directly into the ceramic basin of your slow cooker.

Add the finely diced carrots, celery, yellow onion, diced tomatoes with their juices, tomato sauce, beef broth, Worcestershire sauce, dried Italian seasoning, and smoked paprika into the slow cooker bowl with the beef. Stir firmly to distribute the seasonings evenly throughout the liquid baseline.

Clamp a tight-fitting lid securely over the top and cook on Low for 6 to 8 hours (or on High for 3 to 4 hours).

Exactly 30 minutes before the slow cooker timer finishes, lift the lid and stir the rinsed and drained dark red kidney beans and cannellini beans straight into the bubbling soup, allowing them to warm through completely without breaking apart.

While the beans warm, bring a separate medium pot of heavily salted water to a rolling boil on your stovetop. Drop in the 1 cup of uncooked ditalini pasta and cook according to the package directions until it reaches a perfect al dente chew. Drain the pasta completely and set it aside.

Turn off the slow cooker heat source. Discard any surface oils if desired, adjust with additional salt and black pepper to taste, and stir the cooked ditalini pasta directly into the soup matrix right before spooning into deep bowls. Serve hot with a dusting of freshly grated Parmesan cheese and crusty bread.