In a saucepan, heat the oil. Add the turkey, season with salt and pepper and cook over moderate heat, breaking up the meat, until white throughout, 4 minutes. Add the garlic, onion, chile powders and the cumin and cook, stirring, until fragrant, 5 minutes. Stir in the tomatoes, tomato sauce and 1 cup of water; bring to a simmer. Cook over low heat, stirring occasionally, until thickened, 45 minutes. Add the beans and simmer for 15 minutes.
Meanwhile, light a grill or heat a grill pan. Grill the tortillas over moderate heat until soft, 30 seconds per side; wrap in a towel.
Season the chili with salt and pepper and serve with the grilled tortillas.