Bring about 4 quarts of water to a near boil.
Remove from the heat, add the kombu, and allow it to sit for 5 minutes to soften.
Carefully remove the kombu from the water and gently squeeze out any excess moisture.
Cut the softened kombu into rectangles approximately 4 x 7 inches / 10 x 18 cm.
Place one sheet of kombu horizontally on a bamboo rolling mat. Wet your fingertips and spread about ½ cup / 100 g (3.5 oz) of sushi rice in a thin, even layer over the bottom three-quarters of the kombu.
Drizzle 1 teaspoon (5 ml / 0.2 fl oz) of Sesame Dressing horizontally across the center of the rice.
Arrange 1 piece of kampyo across the dressing, ensuring it extends to both edges.
Sprinkle with ¼ teaspoon of toasted sesame seeds.
With damp fingertips, place your thumbs under the bamboo mat.
Fold the bottom edge of the mat up and over, tucking the edge of the kombu just past the kampyo filling.
Lift the edge of the mat and continue to roll forward, applying gentle, even pressure to create a tight cylinder.
Shape the roll by gently pressing the top and sides with your fingers over the mat to create a squared-off shape.
Place the finished roll seam-side down on a cutting board.
Repeat with the remaining to make 4 rolls.
Using a very sharp knife dipped in water, slice each roll into 6 even pieces.
Serve immediately with extra Sesame Dressing for dipping, if desired.
Keep a plastic-wrapped sheet of nori with your sushi supplies. Use it as a perfect template for cutting the softened kombu to a consistent size.
Keep a small bowl of water (tezu) nearby to dip your fingertips in. This prevents the sticky sushi rice from clinging to your hands while spreading.
Do not over-soak the kombu, as it can become too soft to handle. Five minutes is the sweet spot for making it pliable yet durable.