Drizzle oil in the skillet. Add the onions, peppers, and garlic. Cook until softened. Add the mushrooms and cook a few minutes longer until they are tender. Transfer to a separate bowl.
Season chicken with salt and pepper.
Add the chicken. Brown the chicken on both sides.
Mix the heavy cream, sour cream, and remaining seasonings in a bowl. Season to taste.
Pour over the chicken in the skillet. Cook over low until the chicken reaches 160. Add the vegetables. Serve from the skillet or transfer to a serving platter.
Notes
Chipotle puree - Blend a can of chipotles in adobo. Freeze the remaining puree in an ice cube tray in one tablespoon portions.