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Preheat your oven to 350°F (175°C). Line a baking sheet with parchment paper.
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In a medium bowl, stir together the peanut butter, sugar, and egg until completely combined and smooth. The dough will be thick.
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Roll the dough into 1-inch balls (about 1 tablespoon each) and place them on the prepared baking sheet, about 2 inches apart. You should get about 24 cookies.
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Using a fork, press a crosshatch pattern into the top of each cookie, flattening them slightly. Rotate the fork 90 degrees and press again to create the classic pattern.
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Bake for 10-12 minutes, until the edges are just set but the centers still look slightly soft. Do not overbake — they will continue to firm up as they cool.
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Let the cookies cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely.