Heat a large skillet over medium-high heat and add oil and 2 tablespoons butter.

Meanwhile, season chicken with chili powder, salt, and black pepper. Cook chicken in the skillet on 1 side for 5 minutes, resisting the urge to flip early. Turn and cook, turning occasionally to keep from burning, until no longer pink inside and juices run clear, 10 to 15 minutes, depending on thickness. Transfer chicken to a plate to cool until safe to handle, about 10 minutes. Shred chicken using your fingers and set aside.

Mix remaining 6 tablespoons butter, chicken broth, heavy cream, cream cheese, onion powder, cumin, and hot sauce together in a large, heavy pot. Season with salt and black pepper and bring to a simmer; cook until butter and cream cheese are melted, about 5 minutes.

Add shredded chicken, Monterey Jack cheese, and green chiles to the chili in the pot. Reduce heat to low and cook, stirring occasionally, for 20 minutes.