Place the steak in the freezer for 45 minutes. This will make it easier to slice.
Thinly slice the steak, about five 4-inch-long strips. In a medium bowl, mix the mirin, soy sauce, ginger, chile sauce, lime zest and lime juice. Add the steak and marinate, covered, for at least 2 hours.
Toss the asparagus in the sesame oil. Remove the steak from the marinade. Wrap 2 pieces of asparagus with a single piece of steak. Heat a grill pan set over high heat until smoking. Grill each bundle, turning, until all sides are cooked and the asparagus begins to wilt, about 5 minutes. Sprinkle with the sesame seeds, and then serve.