Cook the sushi rice according to package instructions. Once cooked, mix rice vinegar, sugar, and salt into the rice and let it cool.

Preheat the oven to 400°F (200°C). Toss the eggplant strips with olive oil, soy sauce, and sesame oil. Spread on a baking sheet and roast for 15-20 minutes until tender.

Place a sheet of nori on the sushi mat. Spread a layer of sushi rice over the nori, leaving a small border. Add roasted eggplant, carrot, cucumber, and avocado in a line across the rice.

Using the sushi mat, carefully roll the nori away from you, pressing gently to form a tight roll. Seal the edge with a little water.

Using a sharp knife, slice the rolls into bite-sized pieces. Serve with soy sauce and wasabi on the side.