Bring 2 quarts of water to a boil in a large pot over high heat.
Trim the asparagus ends and cut any very thick stalks in half lengthwise; add to the boiling pot and cook until bright green and crisp-tender, 2–3 minutes, then drain well and spread on a clean towel to cool and dry.
In a medium bowl, whisk the lemon juice and Dijon mustard with the kosher salt and black pepper; slowly drizzle in the extra-virgin olive oil while whisking until emulsified, then stir in the lemon zest and the shallot (finely chopped).
Toss the cooled asparagus with about two-thirds of the vinaigrette to coat and transfer to a platter.
Shave the Parmesan cheese over the asparagus, sprinkle with the fresh parsley, and spoon the remaining vinaigrette on top; serve at room temperature or slightly chilled.