Begin by breaking off the tough ends of the asparagus and discard. Peel the stalks, and lay them on a baking sheet. Drizzle with some olive oil and season with salt and pepper. Roast in the oven until tender, approximately 10 minutes. Cool and cut in half.
To prepare the bread, cut thick slices, and grill or toast in an oven. Once the bread is toasted, rub each slice with the garlic while the bread is still hot.
Using a peeler, shave thin slices of cheese off the wedge, making enough to cover the slices of bread.
To assemble the bruschetta, place asparagus on slices of bread, drizzle with truffle oil, balsamic vinegar, and top with shaved cheese. Serve at room temperature.