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.