Warm oil in a large skillet over medium heat. Add onion and garlic and sauté until softened, about 3 minutes. Turn heat up to medium-high, stir in turkey, salt and chili powder and cook, stirring to break up meat, until turkey loses its pink color, about 5 minutes.
Transfer mixture to slow cooker. Stir in brown sugar, tomato sauce, ketchup, 1/4 cup water and Tabasco. Cover and cook on low until bubbling and flavors have developed, 3 to 4 hours. Serve on buns with pickles or pickle relish, if desired.