If using rectangular aburaage sheets, cut each piece in half lengthwise. Pre-cut square sushi-age can be used as is.
Place the aburaage in a mesh strainer and pour hot water generously over both sides to wash off the surface oil (abura-nuki). Press gently between paper towels to remove excess water.
In a small frying pan or shallow saucepan, combine the water, sake, mirin, sugar, and soy sauce. Bring to a simmer over medium heat, stirring to dissolve the sugar.
Add the aburaage in a single layer. Reduce the heat to low and simmer for 5 minutes, turning halfway through so both sides absorb the seasoning.
Turn off the heat and leave the aburaage in the broth until completely cool — at least 30 minutes. This is when the flavour is drawn deep into the aburaage. Use in kitsune udon, soba, or inarizushi.