In a large bowl, whisk together sugar, applesauce, egg replacer, and vanilla. Stir in raisins. Add the dry ingredients to the wet and mix just until blended. Drop the dough by tablespoonfuls onto prepared baking sheets, spacing cookies about 4 cm apart. Bake for 15 minutes, or until lightly browned.
Transfer cookies to a wire rack to cool.
Makes 3 dozen cookies. They become stale quickly and stick together if stacked. As soon as they are cool, wrap the cookies, layers separated by waxed paper, and freeze. To serve, simply let them thaw to room temperature. Because there is no fat to help them spread, the cookies will be kind of lumpy.