Place the rice in an extra-large bowl with warm water to cover by 3 inches. Swish and rub the rice with your fingers; the water will become cloudy. Drain the rice in a fine-mesh strainer; repeat until the water is clear (up to 5 times). Dry the bowl and reserve.
Place the rice in a medium saucepan with 3 cups cold water and let soak for 15 minutes. Cover the pot with a lid and bring to a boil over medium heat. Watch for steam, then, without lifting the lid, immediately lower the heat to very low and cook, covered, until the rice is tender and all water is absorbed, about 20 minutes. Remove the pan from the heat, fluff the rice with a fork and let stand, covered, for 10 minutes.
Fluff the rice again, then transfer to the reserved extra-large bowl. In a cup, stir together the vinegar and sugar until the sugar dissolves. Drizzle the mixture over the warm rice, then toss well with 2 wooden spoons or rubber spatulas to coat the rice. Cover the bowl with a towel and let the rice cool completely.
Preheat a grill pan or cast-iron skillet over medium heat. Lightly brush the asparagus and shrimp with the oil; season with salt and pepper. Grill the asparagus until crisp-tender, about 4 minutes; set aside. Grill the shrimp until firm and lightly charred, about 4 minutes. When the shrimp is cool, coarsely chop it.
Halve, pit and peel the avocado; cut it into 12 lengthwise strips and place on a plate. Place the asparagus and the shrimp on separate plates. Fill a bowl with water (to dampen your hands so the rice sticks to itself, not to you!). Set the nori on the work surface.
Lay a sushi mat in front of you with the slats running horizontally. (If you have a few mats, break up into teams of 2 or 3 and divvy up these tasks.) Cover the mat with plastic wrap and tuck the plastic under the mats ends to anchor it. Place a sheet of nori, with the long side facing you, on the mat.
Measure out 1 cup of the seasoned rice and place on the nori. With barely damp hands, spread the rice evenly over the nori, pressing it down and smearing it so that it sticks to the nori (A). (If rice sticks to your hands, dampen them again.) Sprinkle 2 tsp. sesame seeds on top.
Teamwork time: One friend holds the plastic wrap down, while the other picks up the nori at 2 corners and gently flips it over so its rice side down (now the rice is on the outside of the sushi).
Across the center of the nori, arrange 2 asparagus spears, making sure they reach both edges. Sprinkle about 1/3 cup chopped shrimp on top. Arrange 2 avocado slices end to end (B). Even rows mean nice, neat rollups!
Untuck the plastic wrap at the end nearest to you and lift it up and forward to force the rice and nori to fold over the filling. Continue forcing the rice to roll up around the filling. Use the plastic wrap to do this, but do not roll the plastic wrap into the sushi roll; it should stay on the outside. You dont want to eat the plastic! Once youve formed the sushi roll, bring the mat up and over it and use both hands on the mat to produce a firm cylinder (C). Repeat this process with the remaining ingredients to make 6 sushi rolls.
Remove the roll and discard the plastic. Use a wet, sharp knife to cut it into 8 pieces (D). Place the sushi pieces flat on a serving plate. Fill small bowls with soy sauce, pickled ginger and wasabi. Now its time for you to help clean up and set the table!