Add everything except the abura-age to a small pot and bring to a boil. Once the sugar has dissolved, add the abura-age and simmer, flipping it several times until most of the liquid is absorbed and the abura-age reaches a deep brown color.
Transfer the contents from the pot to a small bowl and allow it to cool slightly. When it’s cool enough to handle, press out some of the excess liquid. You don’t want to squeeze out all the liquid, just enough to prevent it from being too salty.
Boil a large pot of water and cook the udon for the time specified on the package.
Ensure the noodles are al dente, as they will be sitting in a bowl of hot broth, and you don’t want them to become soggy before you finish eating. When they’re done, rinse them under cold water to stop the cooking process.
To finish, combine the dashi, soy sauce, mirin, and sugar in a pot and heat until it comes to a simmer. Taste and add salt if you feel it needs more. Add the noodles to heat through, then divide them into two bowls.
Top with the seasoned abura-age, scallions, and naruto, then pour the broth over everything. For a little extra color and a kick, you can serve this with shichimi togarashi (Japanese seven-spice chili flakes).