Heat the oil in a large dutch oven over medium high heat. Add the onions and cook them for about 3 minutes before adding the poblanos and mushrooms. Continue to sauté the poblanos, onion, and mushroom mixture for 10-12 minutes. You want the mushrooms to brown on both sides and shrink, but do not allow any of the ingredients to burn.
Season the mushroom mixture with a pinch of salt and black pepper, add the minced garlic, cumin and the chipotle chili powder, if using. Stir to combine, do not allow the seasonings to burn.
Reduce the heat to medium, add the shredded chicken, salsa verde, chicken broth, and hominy into the dutch oven, stir to combine. Kick the heat back up to medium-high, allow the stew to come to a boil, then reduce to heat to low, cover with a lid, and allow the stew to simmer for 12-15 minutes so all the ingredients heat through. Check for seasonings, add additional salt and pepper as desired. Serve stew with desired toppings.