Rinse the shiitake mushrooms under cold running tap water and soak them in a large bowl of cold water overnight.

The next day, remove the mushrooms from the water, reserving the soaking liquid. Put the mushrooms in a medium pot with enough of the reserved soaking liquid to barely cover them. Set the pot over medium heat and bring to a boil; turn the heat to medium-low and cook, covered with a drop lid or a parchment paper disk, for 30 minutes. Skim off any foam that rises during cooking. Add the sugar and cook, covered, for 10 minutes. Add half the soy sauce and continue to cook, covered, for 10 minutes, or until about 85 percent of the liquid is absorbed. Add the remaining soy sauce (shoyu) and the sweet cooking wine (mirin); turn the heat to medium-high and cook the mushrooms, stirring with a wooden spoon, until the liquid is almost absorbed and the mushrooms are coated with a layer of glossy, syrupy sauce. Drain the mushrooms in a strainer and turn them over several times to cool them quickly, discarding the cooking liquid. Store the cooled mushrooms in the refrigerator or freezer. Before using, cut off the stems. The cook can enjoy them as a snack.