Kosher or coarse salt and freshly ground pepperto taste
Heat a very large dry skillet over medium heat. Add the sesame seeds and stir frequently for about 1 or 2 minutes, until they start to become golden. Transfer them to a plate and wipe out the skillet with a paper towel or a dish towel. Trim off the stems, then wipe the caps of the mushrooms with a damp paper towel to clean them. Slice the mushrooms into 1/2-inch slices.
Trim the bottoms off of the asparagus, and if they are thick and the peel is tough, use a vegetable peeler to peel of the outer layer of the asparagus on the bottom half of the stalks. Cut the asparagus into 1-inch pieces.
Heat 1 tablespoon of the sesame oil in a very large skillet over medium heat. Add the mushrooms and the asparagus, season with salt and pepper and sauté for 5 or 6 minutes, until the mushrooms are tender and the asparagus is crisp tender. Drizzle over the remaining tablespoon of sesame oil and toss well. Transfer to a serving dish and sprinkle over the toasted sesame seeds. Serve hot or warm.