Preheat your oven to 375°F. Line a large rimmed baking sheet with unbleached parchment paper and set it aside.
In a medium-size bowl, place the flour, xanthan gum, baking powder, baking soda, and salt, and whisk to combine well. Set the dry ingredients aside.
In the bowl of a stand mixer fitted with the paddle attachment or a large bowl with a handheld mixer, place the butter and beat on medium-high speed for about 2 minutes, then the granulated sugar and continue to beat until light and fluffy (about 5 minutes more).
Add the egg and vanilla, and beat until smooth.
With the mixer running on low, add the flour mixture and beat until just combined.
Remove half of the dough (11 1/4 ounces) and set it aside.
To the rest of the dough, add about 1/8 teaspoon of green or red food coloring (or whatever other food coloring you like). Beat until the color is uniform and vibrant.
Place each piece of dough (the plain and the colored) on a separate large piece of plastic wrap.
Cover the dough loosely, and pat the dough into about a 4-inch square.
Place each on a flat surface, and place in the refrigerator to chill for about 10 minutes or until slightly firm.
Unwrap one of the pieces of dough and place it on a very lightly floured surface.
Sprinkling very lightly with more flour as necessary to prevent sticking, roll the dough into a rectangle about 10-inches square.
Repeat the same procedure, separately, with the other piece of dough.
On a large piece of parchment paper, place the colored square of dough. If the top of the colored square of dough seems very dry to the touch, moisten it very lightly with lukewarm water on your fingertips. This will help ensure that pieces of dough don’t separate much during baking.
Place the plain square directly on top of the colored squares, layering them evenly on top of one another. Roll them to together with gentle pressure to help them adhere.
Starting at one end, roll the layered dough away from you and into a cylinder that is as tight as you can manage.
If any parts of the colored (outside) dough crack during rolling, pinch them lightly together as you work.
Rock the cylinder back and forth to create a uniform cylindrical shape. Wrap the dough tightly in a large piece of parchment paper, cinching the ends.
Chill for at least 20 minutes or until firm enough to slice cleanly.
Once the dough has chilled, rock the cylinder back and forth a bit to reestablish the curve (See Recipe Notes for decoration suggestions here).
Slice the dough by cross-section into about 16, 1/4-inch thick pieces.
If any of the of raw cookie slices seem to have flattened on the bottom, squeeze them gently in an open palm to reestablish the round shape.
Place the raw cookies about 1-inch apart on the prepared baking sheet.
Place in the center of the preheated oven and bake until the cookies are just set in the center (8 to 10 minutes). They should not have browned visibly.
Allow the cookies to cool for at least 5 minutes or until firm on the baking sheet before transferring to a wire rack to cool completely.
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Notes
For flavoring In place of the vanilla extract in this recipe, try using your flavoring oil. I like LorAnn brand, but they’re potent so use sparingly.For the gel food coloring You can only use gel food coloring to color this cookie dough. I always use AmeriColor brand gel food colorings. Do not try to use liquid food coloring in this recipe.For even fancier cookies If you’d like to decorate the outside edge (perimeter) of the cookies, it’s best to decorate the raw rolled dough cylinder before slicing the cookies by cross-section.After chilling, brush the outside of the cylinder lightly with egg white, and sprinkle on your decorating sugar or nonpareils. Roll the cylinder back and forth as you sprinkle the decorations, pressing the cylinder gently to help the decorations adhere. Proceed with the recipe as instructed.