Rinse the turkey necks under cold water and pat them dry. Season the meat by rubbing turkey necks with salt, black pepper, smoked paprika, thyme, and cayenne pepper. Heat vegetable oil in a large pot over medium heat and brown the turkey necks for three minutes per side. Add onions, garlic, bell peppers, and celery and cook until fragrant. Pour in the chicken or turkey broth and bring to a boil. Reduce heat, cover, and cook for two to three hours until the meat is tender. Serve with rice, cornbread, or mashed potatoes for a hearty meal.