Bring the homemade broth (or boxed, if preferred) to a boil in a large pot over medium-high heat. Add the meatballs and spinach and simmer until the meatballs are cooked through and the spinach is tender, about 8 minutes. Whisk the eggs and cheese in a medium bowl to blend. Stir the soup in a circular motion. Gradually drizzle the egg mixture into the moving broth, stirring gently with a fork to form thin stands of egg, about 1 minute. Season the soup to taste with salt and pepper.