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Pre-heat oven to 375°F and line a baking sheet with parchment paper.
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In a large bowl, whisk together the flour, baking soda, and cream of tartar. Set aside.
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In the bowl of a stand mixer fitted with the paddle attachment, cream together the butter, oil, and sugars on medium-high speed until light and fluffy, scraping the sides as necessary.
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Reduce speed to medium and add the eggs, one at a time, mixing just until combined. Add the vanilla and mix until combined.
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Reduce speed to low and add the flour in three additions, scraping down the sides as necessary.
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Drop dough of two tablespoons each onto the baking sheet, spacing two inches apart.
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Bake for 8 to 10 minutes, just until the edges begin to darken. Let cool on baking sheet.