Shape sausage into 42 meatballs. Heat olive oil in a large Dutch oven over medium-high heat. Add meatballs; cook 2 minutes on each side. Remove meatballs from pan. Add onion, carrot, and minced garlic to pan; sauté 4 minutes. Add chicken stock and water; bring to a simmer. Add meatballs; cook 2 minutes. Stir in spinach, pasta mixture, dill, lemon juice, salt, and pepper; cook 2 minutes. Place 1 1/3 cups soup in each of 6 bowls; top each serving with 2 teaspoons grated Parmesan cheese.