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Preheat oven to 350°.
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Lightly oil a cookie sheet and set aside.
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Blend together butters, Splenda and vanilla in a medium size mixing bowl.
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Blend until butter is softened.
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Add egg substitute, water and vinegar.
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Mix briefly.
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Add flours, salt and baking powder.
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Mix using low speed (or by hand) until dough is formed.
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Do not over mix.
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Remove dough from bowl and place on a floured work surface.
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Divide dough in half.
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Pat each half into a circle.
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Cover with plastic wrap and refrigerate about 1 hour, allowing dough to chill.
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Remove dough from refrigerator and roll out on a floured work surface to desired thickness (approximately 1/4-inch).
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Cut with cookie cutters.
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Place cookies on cookie sheet.
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Bake in preheated 350° for 7 to 9 minutes or until slightly browned on the back.
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Cool on a wire rack.