01 - Rinse sushi rice under cold water until water runs clear. Combine rice and water in a saucepan, bring to a boil, cover, and simmer for 15 minutes. Remove from heat and let stand, covered, for 10 minutes. Dissolve sugar and salt in rice vinegar in a small bowl. Fluff rice with a fork and stir in vinegar mixture. Cool to room temperature before assembling.
02 - While rice cools, slice prosciutto into strips, cut fresh mozzarella into thin strips, julienne roasted red bell peppers, and cut sun-dried tomatoes into thin strips. Keep fresh basil leaves and arugula leaves ready for assembly.
03 - Place a nori sheet on a bamboo sushi mat with shiny side down. With wet hands, spread a thin, even layer of cooled sushi rice over the nori, leaving a ¾-inch edge at the top. Arrange prosciutto, mozzarella strips, roasted peppers, sun-dried tomatoes, arugula, and basil in a line along the bottom third of the rice. Drizzle with olive oil and sprinkle with black pepper.
04 - Use the bamboo mat to roll the sushi tightly away from you, applying gentle pressure. Seal the edge with a small amount of water. Repeat with remaining ingredients. Using a sharp, damp knife, slice each roll into 6 equal pieces for a total of 24 pieces.
05 - Arrange sushi pieces on a serving platter. Optionally drizzle with balsamic glaze and garnish with additional fresh basil leaves. Serve immediately at room temperature for best flavor and texture.