Wash the brussels sprouts, trim the ends and remove any discolored leaves. Slice the brussels spouts just as thin as you possibly can with either a food processor or a mandolin. Transfer to a large salad bowl, add the chopped parsley and set aside while you make the dressing.
In a large bowl add the minced garlic, salt and the anchovies. Using the back of a fork, mash and mix the garlic, salt and anchovies until you have a paste. Mix in the mustards and worcestershire sauce. With a small whip mix in the lemon juice, olive oil and the mayonnaise until well incorporated, thick and creamy.
Pour the dressing over the shaved brussels sprouts, add the cashew nuts and toss together.