In a medium bowl, whisk together the red wine vinegar, mustard, sugar and olive oil. Season with salt and pepper, to taste.
Holding the stem of the Brussels sprouts, thinly slice each one until you get to within ½ inch of the stem. Discard the stems and place the sliced Brussels sprouts in a large bowl, breaking them up with your hands and discarding any tough pieces.
Toss the sliced sprouts with the dressing until coated. Let sit at room temperature for at least 15 minutes to allow the sprouts to soften and the flavors to combine.
Before serving, toss in the grated parmesan and taste again for seasonings, adding more salt and pepper, if needed.