Place the pecans in a pan over medium heat. Stir while the pecans roast and get fragrant, about 5 minutes. Add the maple syrup and salt and stir to combine. Cook for an additional 3-5 minutes, until the maple syrup has cooked down. Transfer to a cutting board and let the pecans cool completely. Once cooled, chop the pecans into smaller pieces.
Thinly slice the shallot and transfer to a bowl of ice water for 10 minutes, then drain.
Use a mandoline to thinly slice the Brussel sprouts (if you don’t have a mandoline, use a knife to slice the Brussel sprouts as thinly as possible. Slice the apple into small chunks.
Add the Brussel sprouts, apple, shallot, pecans, pomegranate seeds, and parmesan to a large bowl.
To make the dressing, add all the ingredients to a small bowl. Whisk until everything is well combined and emulsified. Pour the dressing over all the ingredients in the bowl. Mix until well combined and enjoy.