Combine 3 tablespoon of cornstarch and 4 tablespoons chicken broth in a small bowl to make a slurry. Set aside.
Whisk together remaining chicken broth and sour cream. Set aside.
Combine remaining cornstarch and Creole seasoning in a Ziploc bag. Set aside.
Trim chicken breasts of all fat. Horizontally slice chicken breasts into two to three thin slices. Place in Ziploc bag. Shake to thoroughly coat.
Heat the oil in a large skillet over medium-high heat until hot, but not smoking. Add half of the chicken breasts; cook until golden brown on both sides, about 3 to 4 minutes per side. Transfer to a plate lined with paper towels and set aside. Repeat with remaining chicken, adding more oil if necessary.
Add the mushrooms to the skillet; cook over high heat, stirring frequently, until the mushrooms are golden brown around the edges and have given off their liquid, about 3 minutes. Add the Madeira and bring to a boil, scraping to remove any browned bits from the bottom of the pan. Continue cooking until Madeira has reduced by half, about 2 minutes. Add the chicken broth/sour cream mixture; cook for 3 minutes, or until the sauce has thickened slightly. Add the cornstarch/chicken broth slurry; cook stirring constantly until thickened.
Lower the heat to medium. Return the chicken breasts to the pan. Continue to cook until the chicken breasts are heated through, about 2 to 3 minutes. Season to taste with salt and pepper. Garnish with minced parsley or chives and serve immediately. Yield: 4 servings.