1. Prepare an ice-water bath. Bring a large pot of salted water to a boil. Add asparagus; blanch until tender, 3 to 4 minutes. Transfer to ice bath; let cool, then drain on a paper towel-lined plate. Use 1-inch cookie or aspic cutters to shape carrot strips, then add to pot and blanch until crisp-tender, 1 to 2 minutes. Transfer to ice bath and let cool; drain on plate.

2. Whisk together vinegar and mustards; season with salt and pepper. Whisking continuously, add oil in a slow, steady stream.

3. Transfer asparagus to platter. Garnish with carrot cutouts. Serve, with vinaigrette on side.