Preheat oven to 450 degrees. Line a baking sheet with parchment paper for easy cleanup.
Wash asparagus, pat dry, and trim woody ends, usually about 2 inches.
In a small bowl, whisk together olive oil, mayonnaise, Dijon mustard, salt and pepper.
Lay asparagus out on the parchment paper, and pour the dressing over the top, tossing the asparagus around to coat and then arranging into an even layer.
Roast the asparagus in the oven for about 5 minutes (this will depend on the thickness of your asparagus) and then top with Gruyere and breadcrumbs. Return to oven for 4-5 more minutes, watching closely for the breadcrumbs to turn golden brown.