Turn the oven on to 425°F. Spoon 1 tablespoon of olive oil over the poblano peppers on a medium-sized rimmed baking sheet, then toss to coat. Then roast the peppers for 30 minutes, or until aromatic and blistered.
Season the chicken in the meanwhile. The chicken breast pieces, 1 tablespoon olive oil, smoked paprika, oregano, cumin, chili powder, white pepper, and salt to taste should all be combined in a big bowl. If you'd like, put on some disposable gloves and use your hands to thoroughly mix the spices into the chicken. While the peppers roast, marinate the bowl covered and leave away.
Coming back to the peppers, let them a few minutes to cool off before handling. Next, cut off as much of the peppers' papery outer skin and stems as you can. Slice the peppers open gently, then remove the seeds with a spoon. After transferring the peppers to a chopping board, roughly chop them. After that, set aside the chopped poblano peppers.
Melt the butter in a large stockpot or Dutch oven over medium heat. After the chicken starts to sizzle, add the pieces in a single layer to the saucepan while working in batches. For about 3–4 minutes on each side, sauté the chicken until it turns golden brown and becomes caramelized. Next, move the sautéed chicken to a spotless platter using a slotted spoon and put it aside. Continue until all of the chicken has been sautéed and removed from the heat.
Fill the saucepan with the final tablespoon of olive oil. Once heated, add the chopped onion and sauté for 4–5 minutes, or until it is soft and golden brown. After that, add the chopped poblano peppers and garlic, and simmer for a further minute or so, or until the garlic is fragrant.
To coat and cook out the flour, sprinkle it over the mixture and stir thoroughly, approximately 1 minute. Stir thoroughly to mix the sautéed chicken, diced jalapeños, and any remaining juices in the saucepan.Next, gradually add the chicken stock or broth with one hand, stirring with the other to remove any remaining pockets of flour until they are all gone. Allow the mixture to boil for fifteen to twenty minutes.
Next, include the sour cream and half and half, being sure to thoroughly mix them together. Stir thoroughly to properly incorporate the beans, salsa verde, corn, and shredded cheese. For the flavors to fully combine, lower the heat to medium-low and simmer the chili for 20 to 25 minutes.
Spoon the white chicken chili onto individual serving dishes. If preferred, garnish chili right away with diced avocado, chopped cilantro, and fried corn tortilla strips. Have fun!