Rinse the sushi rice under cold water until the water runs clear. Combine the rinsed rice and water in a medium saucepan and bring to a boil. Once boiling, reduce the heat to low, cover, and simmer for 18-20 minutes, or until the rice is tender and the water is absorbed. Remove from heat and let it sit, covered, for 10 minutes.

In a small bowl, mix the rice vinegar, sugar, and salt until dissolved. Gently fold this mixture into the cooked rice, being careful not to mash the grains. Allow the rice to cool to room temperature.

Place a bamboo sushi mat on a clean surface. Lay a sheet of nori on the mat, shiny side down. With wet hands, spread about 1/2 cup of the cooled sushi rice evenly over the nori, leaving a 1-inch border at the top.

Arrange a line of cucumber, bell pepper, avocado, salami, and mozzarella cheese across the center of the rice-covered nori.

Starting at the bottom, use the bamboo mat to roll the sushi tightly away from you, pressing gently to keep the filling in place. Roll until you reach the border of the nori. Moisten the edge of the nori with a little water to seal the roll.

Repeat the process with the remaining nori sheets and fillings. Once all rolls are made, use a sharp knife to slice each roll into 6-8 pieces.

Serve the Italian sushi rolls with soy sauce for dipping.