Heat the olive oil in a large skillet on medium heat. Add the onions, cook until they begin to soften, about 5 minutes.
Add the turkey to the skillet. Cook for about 10 minutes, stirring occasionally, until the turkey meat begins to brown. Add the garlic toward the end of this browning time.
Transfer the turkey and onions to a slow cooker. Add the remaining ingredients, except for the the cheese, to the slow cooker: Hatch chile peppers, tomatoes, kidney beans, and dried spices. Stir to combine the ingredients.
Cover the slow cooker, and cook on low for 7.5 hours.
When the cooking time is done, serve the chili in bowls, topped with the cheese if you are using it. Enjoy!