Preheat oven to 450°.
Place chicken breasts in a large plastic storage bag and flatten to uniform ½ inch thickness using a meat mallet or a rolling pin. Season meat with salt and pepper.
Heat a large ovenproof skillet over high heat. Add oil and tilt pan so that oil covers base of pan. Add chicken to hot skillet and allow to cook for 3-4 minutes or until browned. Turn chicken, taking care to lift any pieces that may have stuck to the pan. Immediately place the pan in the preheated oven. Bake at 450° for 9 minutes or until done. Remove the chicken from pan and transfer to a plate. Keep warm by loosely tenting with aluminum foil.
While the chicken is cooking, heat one tablespoon of butter in a large skillet over high heat. Add the brussel sprouts and mushrooms. Allow to cook, stirring only occasionally, until wilted and slightly brown, about 10 minutes.
Using the pan from the chicken, heat over medium-high heat. Add chicken broth and apple cider. Bring to a boil and scrape pan to loosen browned bits. Reduce heat to medium-low and simmer for about 5 minutes. Whisk in mustard, remaining 1 tablespoon butter, and rosemary.
To serve, top chicken breasts with brussel sprout and mushroom mixture, and then smother with sauce. Serve with roasted vegetables for a delicious, healthy, and low carb meal.