Step 1

In a bowl, mix together the chopped shallots, vinegar, sugar, salt, and pepper. Gradually whisk in the oil. Set the vinaigrette aside.

Step 2

Toast the pecans in a dry skillet over medium-high heat, keeping watch and tossing often, for a few minutes, until lightly browned.

Step 3

Shave the Brussels Sprouts using a food processor with the shredding disc (S blade); a mandoline slicer; or a sharp knife. (See more details in the notes below)

Step 4

In a large bowl, combine brussels, arugula, half the nuts and half the parmesan. Pour about ¾ of the dressing over the salad, toss and taste for seasoning. Add more salt and pepper and dressing, if needed. Sprinkle on the remaining pecans and parmesan and serve.