Heat the oil over medium-high heat in a large heavy-bottomed pot. Sprinkle the chicken with salt and pepper. Brown the chicken on both sides, for a total of 6 minutes. Transfer to a plate.
Saute the garlic, poblano peppers and onions. Add the ancho chile powder, cumin and some salt and pepper to the pot, and saute until tender, about 4 minutes. Return the chicken to the pot and stir in the chicken stock, green chiles and potatoes. Bring to a boil, then reduce to a simmer, and cook over medium heat, stirring occasionally, until the potatoes are tender and the chicken is cooked through, 25 minutes.
Serve in bowls topped with cilantro and cheese if using.
Recipe courtesy of The Neelys