For the tempura batter, place 1 1/4 cups of the club soda in a medium mixing bowl and sift the flour and cornstarch over it. Add the salt and whisk until evenly blended. The batter should be the consistency of thin pancake batter. If necessary, add additional soda water 1 tablespoon at a time to reach correct consistency. Cover and refrigerate for 45 minutes to 1 hour.
Bring a saucepan of water to a boil. Add the asparagus, blanch for 6 minutes, then shock in ice water and drain.
Place a bamboo sushi mat on a work surface with the slats crosswise. Center 1 sheet of nori on the sushi mat. Place a sheet of salmon on top of the nori, leaving a 1-inch border of nori uncovered along the top. Sprinkle 1 teaspoon of black sesame seeds evenly over the salmon and season with salt and black pepper. Place 3 shiso leaves side by side, then add 4 asparagus spears side by side horizontally about 1-inch above the bottom edge.
Grasping the bamboo mat, the nori, and the edge of the salmon on the bottom, tightly roll up, enclosing the asparagus. Firmly press the 1-inch border at the top to create a seal. (The moisture from the salmon will be enough to make the 2 pieces of nori adhere to each other.) The roll should be about 1 3/4 inches in diameter. Carefully remove the bamboo mat, transfer the salmon roll to a plate, and refrigerate.
Repeat with the remaining ingredients, making 2 more salmon rolls. The rolls can be refrigerated for up to 2 hours at this point.
With a serrated knife, cut each of the 3 salmon rolls in half crosswise so that you have 6 (4-inch) rolls.
In a large heavy saucepan, heat 4 inches of vegetable oil to 375 degrees F.
Insert 1 long bamboo skewer crosswise through 1 end of a salmon roll, then insert another skewer through the other end. Using the ends of the skewers as handles, dip the roll into the tempura batter so that it is completely coated, letting the excess batter drip back into the bowl. Carefully immerse the roll in the hot oil, and after 10 seconds, gently push it off the skewers to float free in the oil. Fry until batter is crisp, about 1 to 2 minutes more.
With a skimmer, transfer the first roll to a paper towel-lined plate and keep warm in a very low oven. With the skimmer, remove any leftover bits of batter from the oil so that they don't burn and smoke.
Repeat with the remaining 5 rolls. With a serrated knife, quickly trim off the ends of the rolls and cut each into 5 (3/4-inch-long) rounds.
Make a tall mound of the salad in the center of each of 6 serving plates. Lean 5 pieces of roll against the salad around the base. Dot the remaining 1/2 cup of honey mustard dressing (from the salad recipe) around the outer edge of the plates. Garnish the salad on each plate with a pinch of daikon sprouts.
In a medium mixing bowl, toss the julienned vegetables with the salt, pepper, and 1/2 cup of the dressing. Reserve remaining dressing for garnish.
**Chef's Note for preparing salmon slices: Either ask your fishmonger to cut the salmon sheets for you, or buy a fillet of salmon cut from the tail section (where it is the thinnest) and proceed as follows. Make a guide for your knife by placing large wooden chopsticks about 6 inches apart on a cutting board. Place the salmon fillet between them lengthwise and rest the chopsticks against the long edges of the fish. Holding a very long, sharp filleting knife so that 1 flat side of the blade is parallel to the cutting board, slice the salmon horizontally while steadying the top of the salmon with your other hand. When you have cut one sheet, lift it off the fillet and repeat the process a second and a third time, until you have 3 sheets (the blade may end up resting against the guides). Trim the salmon slices to 4 by 8 inches and reserve the trimmings for another use.
This recipe was provided by a chef, restaurant or culinary professional. It has not been tested for home use.