In a large saucepan or with the stovetop setting on a slow cooker, heat olive oil over medium-high. Add ground turkey, breaking up into small pieces. Add the bell pepper and onion and cook until turkey is no longer pink and vegetables are starting to soften. Add the garlic and cook another minute.
Mix together the spices and sprinkle over the turkey and vegetables. Stir well to coat everything, until fragrant.
Transfer to a slow cooker. Add all remaining ingredients and stir well, making sure pumpkin is mixed through.
Cook on low for 6-8 hours or high for 4 hours. Serve with your favorite chili toppings.