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Preheat the oven to 350°F with a rack positioned in the center. Line three baking sheets with parchment or lightly grease.
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To make the dough: In a small bowl, whisk together the flour, baking powder, and baking soda. Set aside.
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In the bowl of a stand mixer fitted with the flat beater attachment or working in a large bowl with an electric hand mixer, beat the butter, cream cheese, sugar, and salt until combined and smooth, about 2 to 4 minutes at medium speed.
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Add the yolks and extracts and continue beating until combined; stop and scrape down the sides of the bowl as needed.
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Add the sourdough starter and mix until combined.
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Add the dry ingredients and mix until fully incorporated and no dry spots of flour remain.
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To coat the cookies: Place the granulated sugar in a small bowl. Scoop the dough into generous tablespoon-sized portions (about 25g each; a level Tablespoon Scoop works well here). Working with two or three balls of dough at a time, place them directly into the bowl of granulated sugar. Toss to coat, then transfer to the prepared baking sheet, spacing 2" apart, and repeat with the remaining dough.
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Bake the cookies, one baking sheet at a time, for 13 to 15 minutes, until the edges are set. Remove from the oven and allow the cookies to cool completely on the baking sheet while you bake the remaining cookies. Cookies can be served warm or at room temperature.
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Storage information: Store leftover Sourdough Sugar Cookies in an airtight container at room temperature for up to 5 days; freeze for longer storage.