Transfer tofu mixture to a large bowl, add sugar, and beat until slightly frothy. Add oil, applsauce, water, vanilla, and remaining soy-vinegar mixture, and beat until thoroughly mixed. Add dry ingredients and mix untiljust combined. [There may be a few tiny lumps-that's okay.] Cover bowl and chill dough in the refrigerator for at least two hours, or up to 3 days.
Preheat oven to 350 degrees and spray or lightly oil a baking sheet. Drop rounded teaspoonfuls of cookie dough onto baking sheet, about 2 inches apart. Bake in upper third of oven for 10 minutes. Remove from pan and cool on rack. Repeat with remaining dough. Sprinkle cooled cookies with powdered sugar, if desired.
NOTE: Cider vinegar may be replaced with Raspberry vinegar
Makes 3 dozen cookies.