1. the mayonnaise
In a small bowl, whisk together all the mayonnaise ingredients.2. the asparagus
Get the barbecue going!
Place the asparagus on a platter and drizzle with the olive oil. Season with the salt and pepper. (It may seem like a lot of salt, but trust me.) Let it marinate for a while if you wish.
Grill the asparagus over a direct medium-hot heat, until browned and tender, 5 to 6 minutes, turning occasionally.
Arrange on four plates, spoon the mayonnaise on top, and sprinkle with the toasted sesame seeds.