In a large mixing bowl, stir together the sugar, oil and extract. Sift the soy flour, baking powder and salt into the sugar mixture. Add the water and knead to form a dough. Form the dough into a log about 6 inches long, wrap in plastic and refrigerate for at least 2 hours.
Preheat the oven to 325°F. Lightly coat a baking sheet with nonstick spray (or line with parchment paper). Unwrap the chilled dough and cut into ¼-inch-thick slices. Arrange on the prepared baking sheet, spacing about 2 inches apart, and bake until set, about 15 minutes. Cool cookies for 2 minutes on the baking sheet, then transfer to a rack to cool completely.
If desired, frost cooled cookies with a glaze made from 1 cup sifted confectioners’ sugar mixed with 1 to 2 tablespoons of lemon juice.