Heat a small skillet over medium heat. Once hot, add the walnuts. Toast until fragrant, about 3-4 minutes. Add the maple syrup and salt. The maple syrup will sizzle and bubble. Start stirring with a spatula. Once the maple syrup really starts clinging to the walnuts, after about 1 minute, turn off the heat.

Transfer the walnuts to a plate and allow them to cool completely. Once cool, give them a rough chop.

In a jar with a tight-fitting lid, combine the shallot, sherry vinegar, water, salt, pepper, maple syrup, Dijon, grainy mustard, and olive oil. Secure the lid and give it a good shake to combine. Set aside.

Remove the rough exterior from the celery root. From here, cut it into 4 wedges. Run each wedge on a very thin setting of your mandoline slicer. It should be paper thin! Transfer celery root to a large bowl.

Adjust the mandoline slicer to a slightly thicker setting. Cut the fennel bulb in half and remove the core. Slice the fennel on the mandoline and transfer to the large bowl.

Remove the core of the apple and slice on the mandoline. Transfer the apple to the large bowl.

Slice the celery as thin as you can with a knife and transfer to the bowl. Chuck the inner celery leaves in there. Chop the parsley and add to the bowl as well.