Add the rice to a mixing bowl and cover it with one or two inches of cold water. Scrub the rice with your fingers, rubbing the grains against one another, until the water turns cloudy. Drain the rice and repeat until the water stays clear after scrubbing.
Drain the rice in a sieve and let it stand for 30 minutes. Add the rice, water, and kombu (if using) to a saucepan.
Soak the rice until it turns a few shades whiter, about 30 minutes to one hour. Bring the rice to a boil over high heat and cover it with a lid.
Reduce the heat to low and cook the rice for 15 minutes. Moisten the paddle and the interior of the hangiri with a mixture of one part vinegar to three parts water.
Take the rice off the stove and discard the kombu. Let the rice stand, covered, for 20 minutes. Don't lift the lid at any point.
Mix the vinegar, sugar, salt, and mirin or sake (if using) until the sugar dissolves. Fluff the rice using the paddle after 20 minutes and replace the lid. Don't scrape any sticking rice off the bottom of the pot.
Steam the rice for five more minutes and transfer it to the hangiri. Spread the rice in an even layer and add the seasoned vinegar over the top.
Mix the rice using a side-to-side cutting motion with the edge of the paddle to prevent crushing the grains. At the same time, cool the rice using a hand fan or an electric fan. Lay a moist paper towel under the hangiri (or bowl) if it slides around.
Mix the rice until it's just warm. Cover the rice with a moist paper towel until serving. Serve the rice while slightly warm or just above room temperature.