Heat oven to 375°. Place chicken breast into a shallow baking dish and sprinkle with the salt and pepper, then drizzle with olive oil. Bake for 35-40 minutes or until chicken reaches 165 degrees.
While chicken is baking, thinly shred the brussels sprouts using a mandolin. Chop the romaine, dice the apple and set everything aside.
In a heavy bottom skillet, fry the bacon over medium heat until crisp. Let cool on a paper towel lined plate. Then crumble into bits and set aside.
Make the dressing by whisking the remaining olive oil, salt and pepper with dijon mustard and apple cider vinegar until emulsified.
Using two forks, shred the chicken breast in its baking dish, tossing in the juices.
Place the produce, bacon and chicken into a large mixing bowl, pour dressing over top and toss until well coated. Divide onto serving plates and enjoy!