If you have fresh broccoli instead of frozen, cook it a little longer than the frozen version, which is often already par boiled. Slideshow: More Turkey Soup Recipes
In a large heavy pot, heat the butter over medium heat until hot, stir the onions, garlic, 3/4 teaspoon salt, and 1/2 teaspoon pepper and cook, stirring occasionally, until golden, 8 to 10 minutes. Stir in the turkey meat, stock, band broccoli bring to a gentle boil. Season the soup with salt and pepper and serve.