Combine all of the dressing ingredients in a jar and shake until well combined. Set aside.
Place the shaved Brussls sprouts, lettuce, shredded chicken, sliced apple, dried cranberries, pepitas, and goat cheese in a large serving bowl.
Pour the dressing over the salad and toss to coat evenly. Let rest at room temperature for about 15 minutes before serving so the Brussels soak in the dressig a bit.