Mix dry ingredients, then add butter and cheese, just mixing until pea sized pieces form. Add egg to water, mix well, then add to dry ingredients, mixing until a dough forms. Add a little more water only if dough will not form without it. Divide dough in half, forming into 2 disks, wrap in plastic, and chill for at least one hour.
Roll out dough between plastic and parchment to about 1/8-inch thick. Cut using a straight edge into 1/4-inch to 3/8-inch strips. Transfer parchment onto half sheet pan. Carefully stand the strips on their thin sides and form them into waves (Chef's note: Though traditionally twisted to form straws, we made waves with ours).
Bake at 400° for 10 to 12 minutes, until just starting to color. Remove pan from oven and place on cooling rack. Allow Cheese Straws to cool before serving.
Chef's Note: A fun way to serve the Cheese Straws is to stand them on end in a heavy glass, like bread sticks.
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