Rinse the sushi rice in cold water several times and then soak it in cold water for 30 minutes. After soaking, cook the sushi rice in accordance with the package directions.
Preheat your oven to 425º.
Spread the cut eggplant out on a baking sheet or large cutting board and sprinkle with the salt. Allow the eggplant to rest for 10 minutes. The salt will draw the moisture out of the eggplant.
While the eggplant is resting, prepare the miso glaze by combining the sesame oil, mirin, light miso paste and maple syrup in a small food processor. Pulse until smooth and set aside.
When the eggplant is finished resting, blog the eggplant with a clean kitchen towel and toss it in 1 tbsp safflower oil. Lay the eggplant out on the prepared baking sheet, being careful to keep the pieces separated. Roast the eggplant on the middle rack for 10 minutes. Pause to flip the eggplant and then roast for 10 minutes more.
While the eggplant is roasting, prepare the sushi rice. Combine the unseasoned rice vinegar, white sugar and salt in a small sauce pan. Bring the mixture to a boil and whisk until the salt and sugar are dissolved. Fold the mixture into the cooked rice and then spread the rice out on a baking sheet to cool.
Remove the roasted eggplant from the oven and turn on the broiler. Using a basting brush, brush the marinade on to the eggplant and return the baking sheet to the oven. Broil the eggplant until the miso glaze has caramelized and browned. About 1-2 minutes. Remove the baking sheet from the oven.
Make the sushi rolls by laying 1 sheet of nori on the bamboo rolling mats. Wet your hands (this keeps the rice from sticking to your hands) and add 1/4 of the rice to the nori. Using the rice spreader or your hands, spread the rice out on sheet of nori, creating a thin layer of rice. Place a row of roasted eggplant and sliced avocado about 1/3rd of the way from the bottom of the nori sheet. Starting at the bottom of the mat, roll the mat up and over the filling. Gently press and then continue to roll. Unroll the mat and then use a sharp, wet knife to slice the roll into 6-8 pieces. See my blog post for visual instructions.
Top with sesame seeds, if desired, and serve with tamari, wasabi paste and pickled ginger.