Cut the daikon into rounds about 1-1 ¼ inches (2.5-3 cm) thick. Peel each piece thickly, removing about ¼ inch (5 mm) of the outer layer along with the skin.
Trim the sharp edges around the circumference of each daikon round on both sides to create a slightly rounded shape. On one cut side of each piece, make a shallow cross-shaped incision about ¼-⅓ of the way through.
Arrange the daikon rounds in a pot and add enough water to fully submerge them, leaving enough room for the pieces to move freely. Bring the water to a boil, then reduce the heat to low to maintain a gentle simmer, with small bubbles continuously rising to the surface. Cook for about 30-40 minutes, until the daikon is tender. (To check for doneness, insert a skewer into a piece of daikon. It should slide in easily.)
Carefully remove the daikon from the pot, taking care not to break the pieces, and discard the cooking water. Return the daikon to the pot and add enough fresh water to fully cover the pieces, along with the kombu. Bring to a boil, then reduce the heat to very low, keeping the water just below a simmer. Cook for about 30 minutes to allow the daikon to gradually absorb the umami from the kombu.
Meanwhile, combine the miso, sake, mirin, and sugar in a saucepan, stirring until the miso is dissolved. Place the saucepan over medium heat and bring the mixture to a gentle simmer. Once it begins to simmer, reduce the heat to low and cook for about 3 minutes, stirring occasionally with a spatula, until the sauce thickens.
Carefully transfer the daikon to serving plates and spoon the miso sauce over the top.