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In a medium bowl, combine flour, baking powder, and salt. Set aside.
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Add mint leaves and granulated sugar to the bowl of a food processor. Pulse until the mint is finely chopped. Add the butter and pulse until combined.
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Add the flour mixture and pulse to combine. Add the egg and egg yolk. Pulse until a dough forms.
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Turn dough out onto a lightly floured surface and knead into a ball. The dough might be a bit wet and sticky. Divide the dough in half and shape each half into a disk, about 1 inch thick. Wrap disks in plastic wrap and chill in the refrigerator until firm, at least 2 hours.
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Once dough has chilled, preheat oven to 350 F. Line two baking sheets with parchment paper. Set aside.
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Remove 1 disk of dough from the refrigerator and roll out on a lightly floured surface, to about ¼ inch thickness.
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Cut out rounds using the fluted round cookie cutter. Cut out a small circle in the center of the round using the small round cookie cutter. Transfer cut cookies to prepared baking sheets. Repeat with second disk of dough.
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Bake for 10-12 minutes, until edges are lightly brown. Cool for 2 minutes on the baking sheet before transferring to a wire rack to cool completely.