In a large bowl combine eggs, onion, bread crumbs, cheese, parsley, 1/2 teaspoon of the salt, and 1/2 teaspoon of the pepper. Add ground beef; mix well. Shape mixture into forty 1-1/4-inch meatballs. In a large skillet heat oil; brown meatballs, half at a time. Drain on paper towels.
In a 5-to 6-quart slow cooker combine broth, carrots, dried oregano (if using), the remaining 1/2 teaspoon salt, and the remaining 1/4 teaspoon pepper. Gently add meatballs.
Cover and cook on low-heat setting for 6 hours or on high-heat setting for 3 hours, stirring in fresh oregano (if using), pasta, and escarole during the last 20 minutes of cooking. Ladle into bowls. If desired, garnish with oregano sprigs. Soup will thicken upon standing.