01 - Rinse sushi rice under cold water until water runs clear. Combine rice and water in a saucepan, bring to a boil, then cover and simmer for 15 minutes. Remove from heat and let stand covered for 10 minutes. Dissolve sugar and salt in rice vinegar, then fluff rice with a fork and stir in the vinegar mixture. Cool to room temperature before assembling.
02 - While rice cools, slice prosciutto into thin strips. Cut fresh mozzarella into thin strips. Slice roasted red bell pepper into thin strips. Julienne sun-dried tomatoes. Wash and pat dry fresh basil and arugula leaves. Keep all components separated and ready for assembly.
03 - Place a nori sheet on a bamboo sushi mat with shiny side facing down. Moisten hands and 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 horizontal line along the bottom third of the rice. Drizzle with olive oil and sprinkle with black pepper.
04 - Using the bamboo mat, roll the sushi tightly away from you, applying gentle pressure to maintain the cylindrical shape. Seal the edge with a small amount of water. Repeat with remaining ingredients to form 4 rolls. Using a sharp, damp knife, slice each roll into 6 equal pieces, wiping the blade clean between cuts.
05 - Arrange sliced sushi rolls on a serving platter. Optionally drizzle with balsamic glaze and garnish with additional fresh basil leaves. Serve immediately while rice remains at room temperature. For best results, consume within 2 hours of assembly.