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In a medium bowl, beat butter, granulated sugar, and light brown sugar together until light and fluffy.
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Add egg, cream of tartar, baking soda, salt, and vanilla and beat until combined.
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Gradually add in the flour, beating until combined. Divide the dough into four sections.
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Dye the sections of dough orange, teal, pink, and purple by kneading a few drops of gel food coloring into each section. Aim to have one color per dough section.
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Wrap each section of dough in plastic wrap and chill for 15 minutes.
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Preheat the oven to 375 F. Line two baking sheets with parchment paper.
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Take some pieces of each color of dough and roll into a ball. Aim to have a 1-inch ball, but they can be a little bigger. Place the dough balls onto the prepared baking sheet, a couple inches apart.
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Chill dough balls for 15 minutes before baking.
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Bake for 9-12 minutes or until the edges are just starting to brown.
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Let cookies cool for two minutes on the baking sheet before transferring to a wire rack to cool completely.