Preheat oven to 350 degrees F. Lightly oil a cookie sheet and set aside.
Blend together butters, Splenda Granulated Sweetener and vanilla in a medium mixing bowl with an electric mixer, or by hand. Blend until butter is softened. Add egg substitute, water and vinegar. Mix briefly. Add flours, salt and baking powder. Mix on low speed, until dough is formed. Do not overmix.
Remove dough from bowl and place on a floured work surface. Divide dough in half. Pat each half into a circle and cover with plastic wrap. Refrigerate approx. 1 hour, allowing dough to chill.
Remove dough from refrigerator and roll out on a floured work surface to desired thickness, approx. 1/4 inch. Cut with cookie cutters. Place cookies on prepared sheet.
Bake in a preheated 350 degrees F oven 10-12 minutes or until lightly browned on the back. Cool on a wire rack.