First make your rice. Rinse the rice in a fine mesh strainer until the water runs clear. Put the rinsed rice and water in a medium saucepan and bring to a rolling simmer. Reduce to a mild simmer, cover with tight fitting lid, and cook until rice is completely cooked, about 15 minutes. You can also cook the rice in a rice cooker per manufacturer's instructions.
While the rice is cooking, heat the vinegar, sugar and salt and mix until sugar and salt are dissolved, and set aside.
Roast your peppers. Place whole peppers over gas stove burner and blacken on all sides. The same can be done on a gas grill, or by rubbing the peppers with olive oil and roasting in a 400° oven until they are blistering. Place the blistered-blackened peppers in a bowl and cover tightly with plastic.
When the rice is done, mix with the warm vinegar mixture and set aside. Allow to cool to room temperature before making sushi.
Completely clean the burnt skin off the roasted peppers under running water. The remaining pepper should be the cooked, sweet flesh of the pepper. Cut the peppers into sushi piece sizes, for making individual sushi, not rolls.
Cut open the avocado and slice into very thin slices.
Place a bowl or spray bottle of cool drinking water near your work surface. Use the water to moisten your hands, and then take a small fistful of rice and shape into a sushi-sized log-shaped base. Your avocado and pepper will go on top of these eventually. Clean your hands, re-moisten hands with water, and repeat until all the rice is used up and you have many sushi rice bases. You will find the rice is just sticky enough to squeeze into the shape you want. You can experiment with a disc or other shape if you want. Have fun and don't make it more difficult than it actually is.
Once you have your rice bases, place a slice of avocado on top of each rice base, then place a slice of roasted pepper on top of the avocado. You should have about 16-22 pieces of vegan sushi once you are all done.
Serve with ponzu, soy sauce, or other favorite sushi dipping sauce. Top with fresh cilantro, daikon sprouts, or chives for extra garnish, if desired.