First make the dressing by combining all the ingredients in a bowl and mix together until it is completely blended. Taste the dressing and adjust the seasoning if needed.
Wash and chop the ends off the Brussels sprouts. Then cut them in half. Add the brussels sprouts to a food processor and pulse until they are chopped up. You want it to have a "crunchy" texture so don't over process it. Roughly chop the walnuts with a knife.
Put the Brussel sprout, nut and arugula in a large bowl. Pour the dressing on top and toss together covering all the salad. Taste again to see if you want to adjust any of the ingredients. Serve immediately and enjoy!