Melt butter in a pot over medium heat. Place onions in the pot and cook until tender. Stir in carrots and celery; cook until tender. Stir in potatoes and flour. Pour in chicken stock and season the soup with marjoram.
Place turkey in the pot and bring to a boil. Reduce heat to low, cover, and simmer for 30 minutes.
Mix green bell pepper into the soup and continue cooking until pepper is tender, about 10 minutes.