Brown the Meatballs: In a large skillet or Dutch oven, heat 1 tablespoon of olive oil (or enough to coat the bottom of the pan) over medium-high heat. Place half of the meatballs in a single layer in the pot. Cook the meatballs until nicely browned, about 1-2 minutes per side (they do not need to be completely cooked through). Transfer the meatballs to a tray and repeat with additional oil and remaining meatballs. Set browned meatballs aside.
Add Ingredients to the Slow Cooker: Place the carrots, celery, onion, garlic and bay leaf in the bottom of a slow cooker. Add the browned meatballs on top and pour 8 cups of broth over top (this is less broth than the stovetop method, because the slow cooker adds a lot of condensation back into the soup).
Cook: Cover and cook on LOW for 4-6 hours or on HIGH for 2-3 hours, or until the vegetables are tender and the meatballs are cooked through.
Add Pasta: During the final 15-20 minutes of cooking, stir in the dry pasta. Cover and continue cooking until the pasta is tender.
Stir in Spinach: Add the spinach to the pot at the very end and stir just until the leaves wilt. Taste and season with salt and pepper as needed.
Serve: Ladle into bowls and garnish with grated Parmesan cheese, a squeeze of fresh lemon juice, and/or chopped fresh herbs.