Preheat the oven to 350°F. Line large-rimmed baking sheets with parchment paper.
In a medium bowl, whisk together the flour, baking soda, baking powder, and salt.
In the bowl of an electric mixer, beat the butter, caster sugar, and brown sugar on medium-high speed until smooth and well combined, about 2 minutes. Scrape down the sides and bottom of the bowl. Beat in the peanut butter until well combined. Beat in the egg and vanilla. On low speed, gradually add the flour mixture, beating until combined.
4. Place the caster sugar for rolling in a separate small bowl. Using a medium spring-loaded cookie scoop, form the dough into 1 1/2 tablespoon rounds. Roll between your palms to smooth, then roll in the granulated sugar before placing on the prepared baking sheets, spacing about 2 inches apart. Slightly flatten the dough by pressing the back of a fork into each ball of dough twice, to create a criss-cross pattern.
Bake for 10 to 12 minutes or until the edges are slightly browned. Let cool on baking sheets for 10 minutes before removing the cookies to a wire rack to cool completely.
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