Combine the lemon zest, lemon juice, shallot, mustard, and salt and pepper in a bowl. Meanwhile, toast the pine nuts in a medium pan over medium heat, stirring often, until golden brown, 3 to 5 minutes. Remove to a small bowl to cool.

Using a vegetable peeler, thinly slice the asparagus lengthwise into strips and place in a large bowl. (If you have any trouble peeling the asparagus, place the spear on the flat wooden handle of a spatula. This will lift it high enough to allow the peeler to move freely.)

Whisk the olive oil into the lemon-vinegar mixture in a thin and steady stream. Taste and season the dressing with salt and pepper.

Add the reserved pine nuts, dressing, half of the Parmesan, and the parsley to the asparagus and toss to combine. Taste and season with salt and pepper. Let sit at least 10 minutes before serving.