Rinse the rice thoroughly under cold water until the water runs clear.
If using a rice cooker, combine the rice and water in the rice cooker and cook according to the manufacturer's instructions. For stovetop cooking, combine the rice and water in a medium saucepan. Bring to a boil over medium-high heat, then reduce to low heat, cover tightly, and simmer for 15 minutes. Remove from heat and let sit, covered, to steam for an additional 10 minutes.
Transfer the cooked rice to a large bowl or hangiri and allow it to cool slightly until it is warm but comfortable to handle.
Mix the tamari, mirin, sugar, and sesame oil into the rice, stirring gently to avoid smashing and smushing the grains.
To shape the onigiri by hand, lightly dampen your hands with water and sprinkle a small amount of salt onto your palms to prevent sticking. Take a handful of seasoned rice and gently press it into a triangular shape, tucking 1 umeboshi plum into the center, if desired. Repeat with the remaining rice. If using an onigiri press, follow the manufacturer’s instructions, ensuring the rice is packed evenly and firmly, without using so much pressure that the rice grains get smushed.
Lightly dust the formed onigiri with potato starch on both sides.
Stir together the tamari, and mirin in a small bowl. Heat a non-stick or cast-iron skillet over medium heat.
Lightly oil the skillet with sesame oil and place the onigiri in the pan. Cook until the surface is lightly crisp and golden, then brush the glaze evenly over both sides of the onigiri. Continue to cook, flipping occasionally, until the glaze caramelizes and the onigiri develops a deeper golden color.
Serve warm, optionally garnished with sesame seeds or alongside pickled vegetables.