01 - Rinse sushi rice under cold running water until water runs completely clear, about 3-4 minutes. Combine drained rice and 2 cups water in a medium saucepan. Bring to a rolling boil over high heat, immediately reduce to low, cover tightly, and simmer for 15 minutes until water is absorbed. Remove from heat and let stand, covered, for 10 minutes. Meanwhile, whisk together rice vinegar, sugar, and salt until dissolved. Transfer cooked rice to a wide shallow bowl, fluff with a fork, and gradually fold in vinegar mixture while fanning to cool. Let rice reach room temperature before assembling.
02 - While rice cools, prepare all fillings for assembly. Slice prosciutto into 2-inch wide strips if needed. Cut mozzarella ball into thin ¼-inch wide strips. Julienne the roasted red bell pepper into matchstick-sized pieces. Drain sun-dried tomatoes well and slice into thin strips. Wash and thoroughly dry basil leaves and baby arugula. Keep all components separated on a cutting board or platter for easy access during rolling.
03 - Place one nori sheet on a bamboo sushi rolling mat with the shiny side facing down. Lightly moisten hands with water and spread a thin, even layer of seasoned sushi rice over the nori, leaving a 1-inch empty border at the top edge. Arrange fillings in a horizontal line along the bottom third: layer prosciutto (or zucchini), mozzarella strips, roasted peppers, sun-dried tomatoes, arugula, and basil. Drizzle with ½ teaspoon olive oil and season with freshly ground black pepper.
04 - Using the bamboo mat, lift the edge closest to you and roll tightly away from your body, applying gentle pressure to form a compact cylinder. Seal the roll by moistening the exposed nori edge with water and pressing firmly. Repeat with remaining nori, rice, and fillings to make 4 rolls. With a very sharp knife dampened with water, slice each roll into 6 equal pieces, wiping the knife clean between cuts. Arrange sliced pieces cut-side up on a serving platter.
05 - Drizzle assembled sushi with balsamic glaze if desired and garnish with additional fresh basil leaves. Serve immediately at room temperature for best texture and flavor. For entertaining, arrange on a large platter with small bowls of extra balsamic glaze on the side for guests.