Place sausage in an oven-safe skillet over medium heat. Poke holes into the sausage with a fork. Cook, turning as needed, until browned and firm, 5 to 7 minutes. Transfer to a plate and let cool to room temperature.

Preheat the oven to 400 degrees F (200 degrees C).

Season chicken breasts with salt, pepper, and cayenne. Refrigerate sausage until ready to use.

Heat oil in the same skillet over medium-high heat. Sear chicken breasts, skin-side down, until browned, 5 to 6 minutes.

Meanwhile, cut off the base of the mushrooms and separate individual segments. Dice cold sausage.

Flip chicken breasts over and sear on the opposite side, 2 to 3 minutes more. Set aside on plate.

Add red onion, sausage, and mushrooms to the skillet. Season with salt. Cook and stir until mixture begins to brown, about 5 minutes. Turn off heat and return chicken to the skillet, skin-side up.

Bake in the preheated oven until chicken is no longer pink in the center and the juices run clear, about 15 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).

Transfer chicken to serving plates. Cover skillet handle with a towel; place over high heat. Cook and stir sausage mixture until caramelized, about 1 minute. Pour in wine and simmer until reduced by about half, about 2 minutes. Reduce heat to low and toss in butter and 1 tablespoon parsley. Stir frequently until butter melts.

Spoon sauce over the chicken. Garnish with remaining parsley.