Crumble up the soy milk lees if they are extremely compact. Set aside.

Heat the oil in a medium nonstick skillet over medium heat. Add the shallot and cook, stirring, for 5 to 8 minutes, until turning golden, as sign of near crispness. Use a slotted spoon to transfer the shallot to paper towel to drain. Keep the oil in the pan.

Increase the heat to high, add the lees. Cook, stirring frequently, for 4 to 5 minutes, until they have gone from being damp clumps to a fluffy, fine mixture, like fresh breadcrumbs. Incorporate any crusty bits that form at the bottom and sides of the skillet.

Add all the vegetables and dashi stock. Cook, stirring to ensure even cooking, to concentrate the flavor. The lees will suck up the moisture and feel like mashed potatoes. Keep stirring the vegetables are tender-crisp. Add dashi or water by the tablespoon to further cook, if needed.

Transfer to a bowl set aside to cool completely. Refrigerate if you want to hasten the process. If not serving right away, cover with plastic wrap and chill. Return to room temperature before moving ahead.

Before serving, mix in the mayonnaise. Season with drops of soy sauce and pinches of salt and sugar. Add dashi by the tablespoon to moisten, as needed. When satisfied, mix in about half of the shallot. Pile the mixture on serving plates and sprinkle on the remaining shallot. Eat with fork or chopsticks.