Place asparagus spears in a resealable plastic bag.
Whisk olive oil, vinegar, and mustard in a bowl. Pour over asparagus in the bag and distribute evenly. Marinate for 1 hour.
Preheat the oven to 400 degrees F (200 degrees C).
Divide asparagus into bundles of 3 stalks each. Cut prosciutto slices in half lengthwise and lay on a cutting board. Wrap a piece of prosciutto around each bundle to create 7 or 8 bundles. Place bundles in a 9x13-inch baking dish.
Bake in the preheated oven until asparagus is tender, 14 to 16 minutes.
Remove dish from oven and set oven to broil. Place 1 slice of Brie cheese on top of each bundle and sprinkle with crushed walnuts. Return to the oven and broil until cheese begins to melt, about 1 minute.
