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Whisk together the flour, baking soda, baking powder and salt. Set aside.
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Cream the butter. Scrape down the sides and bottom of the bowl, and then beat in the brown sugar. Scrape again and beat in the sugar. Beat until light and fluffy, about 3 minutes.
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Scrape down the sides and bottom of the bowl, and beat in the peanut butter until completely blended.
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Beat in the egg and then the vanilla, scraping the bowl as needed.
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Mix in the flour mixture, 1/3 at a time.
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Press plastic wrap or wax paper down onto the dough and then cover the bowl. Chill in the refrigerator for at least 2 hours, preferably overnight (my compromise is to bake a few cookies off after 2 hours but the save the rest for later).
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When you are ready to bake, preheat the oven to 350 F. Line your baking sheets with parchment paper or a silicone mat. Place about 1/4 cup of granulated sugar into a small dish.
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Scoop balls of cookie dough about 2 tablespoons in size, roll them quickly into a ball, and place them on the baking sheet at least 2 inches apart--I like 6 cookies to a sheet.
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Lightly wet the bottom of a drinking glass or a cookie stamp. Press the glass or stamp into the sugar and then press a cookie down to flatten it just a bit--not a lot. Repeat.
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The cookies will have some sugar on the top--great. Also sprinkle them with a smattering of coarse or flaky sea salt.
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Bake for 12-14 minutes, until the cookies are set and starting to brown at the edges (I like mine less done, and then I let them cool completely on the pan).