Heat 1 tablespoon of the oil in a large saucepan over medium heat. Add the onions and cook, stirring frequently, until soft, about 8 minutes. Add the green pepper, 1/2 teaspoon of the salt, 1/4 teaspoon of the pepper, and the mushrooms. Continue cooking until the mushrooms give up their liquid, about 6 minutes, and are tender. Place the vegetables in a colander, reserving both vegetables and liquid. You should have about 1/2 cup of liquid. Return pan to heat and add the remaining 1 tablespoon of oil. Season the chicken with the remaining 1 teaspoon of salt and 1/4 teaspoon of pepper. Cook the chicken in batches until golden brown and cooked through, about 5 minutes. Add it to the vegetables. Pour the wine, broth, and vegetable liquid into the pan and bring to a boil. With a wooden spoon, loosen any brown bits stuck to the pan and let cook in the sauce. Add the barbecue sauce, Worcestershire, mustard, and hot sauce. Whisk until smooth. Boil until the liquid has reduced by half, to about 11/4 cups. The liquid should thicken slightly. Reduce heat and whisk in the sour cream. Do not let the sauce boil. Return the vegetables and chicken to pan and simmer until heated through. Serve over rice, pasta, or toast.