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Bring butter, shortening, and eggs to room temperature.
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Mix brown and granulated sugars together in small bowl.
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In medium-sized bowl, sift or sieve the dry ingredients (all-purpose flour, coconut flour, cornstarch, baking powder, baking soda, fine sea salt, and cardamom).
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In bowl of stand mixer fitted with paddle attachment, cream the butter and shortening at medium-high speed until smooth and creamy, about 1 minute. With mixer set at low speed, gradually add the granulated and brown sugars then beat on medium-high speed for 2 minutes, stopping periodically to scrape down sides of bowl as necessary. Mix in the whole egg and beat for a few seconds to incorporate, stopping if necessary to scrape down sides of bowl. Repeat with the egg yolk and, lastly, add the vanilla. Do not overbeat mixture.
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With speed of mixer set to lowest speed, gradually add the dry ingredients and mix just until ingredients are combined. Do not overmix. Remove bowl from mixer stand and stir in the rhubarb, pistachios, and white chocolate chips.
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Cover bowl tightly with plastic wrap or, alternatively, transfer dough to bowl that has airtight cover and refrigerate dough for at least 2 hours and, ideally, for 24-48 hours.
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To bake, remove dough from refrigerator and let cookie dough sit at room temperature for about 10-15 minutes, or just until dough can be scooped up to form cookies. Do not let cookie dough warm up completely to room temperature.
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Position oven rack in center of oven and preheat oven to 350°F. Line baking sheets with parchment paper.
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Using either a cookie scoop or two tablespoons, scoop up dough (about 1 1/8 oz per cookie) and transfer to prepared baking sheet, spacing cookies 2” apart. Bake for 14-18 minutes (depending on cookie size and oven), or until cookies have puffed up, have the appearance of the tops starting to look dry, edges set, and the cookies are slightly tanned. Rotate cookie sheets at the halfway point during baking. For soft-textured cookies, do not overbake. Remove cookies from oven and cool completely on cookie sheet (i.e., about 30 minutes).