Make the dressing: In a lidded jar, combine the mustard, olive oil, lemon juice, honey, salt, and pepper. Seal tightly and shake vigorously to combine. For a creamier dressing, whiz in a blender. Store in an airtight container, chilled, for up to 2 weeks.
Make the asparagus: Fire the grill to medium-high heat and position the grill grate 2 to 4 inches above the coals.
While the asparagus are still bundled, slice off about 2 inches from the fibrous bottoms.
Rinse the asparagus, allowing a few water droplets to cling to the stalks, and transfer to a serving plate or baking sheet; the moisture will help them steam and cook over the fire. Add the olive oil and, using long tongs or your hands, toss the asparagus until evenly coated with the oil. Season with the salt and pepper.
Place the asparagus on the grill grate over direct heat. Using long tongs, rotate the asparagus frequently and cook until tender and charred, 5 to 10 minutes. Be careful not to let any fall through the grate.
Transfer the grilled asparagus to a serving plate, baking sheet, or campers' plates and drizzle with the dressing. Set out the Parmesan wedge with a vegetable peeler so campers can add thin shavings of cheese to their dish.
Serve warm or cold. Store leftovers in an airtight container, chilled, for up to 4 days.