Combine the carrots, lemon zest, dill sprigs, olive oil and 1/2 teaspoon salt in a 5-to-6-quart slow cooker. Season the chicken with salt and add to the cooker. Add the broth and 4 cups water, cover, and cook on low, about 8 hours.
About 20 minutes before serving, add the pasta to the slow cooker, cover and cook until tender, about 15 minutes.
Stir the chopped dill, peas and spinach into the soup and cover until the spinach wilts, about 2 minutes. Stir to break up the chicken and season with salt and pepper. Ladle into bowls and crumble the feta on top. Serve with lemon and bread, if desired.