Spread walnuts on a cookie sheet and bake until they have some color to them and are fragrant, about 5 to 8 minutes. Allow walnuts to cool enough to chop.
In a large salad bowl or mixing bowl, whisk together the walnut oil, lemon juice, lemon zest, cider vinegar, mustard and salt until smooth.
Wash the Brussels sprouts, chop off all of the hard stems and remove the leaves that fall off easily.
Slice Brussels sprouts from tip-to-tail (not length-wise). Stop slicing once you get to the hard white part – this part you can either discard or chop finely.
Using your hands, break apart any slices of sprouts that are stuck together (this can usually be achieved by simply tossing the shaved Brussels sprouts)
Add shaved Brussels sprouts to the bowl with the dressing and toss together until Brussels are completely coated.