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Preheat oven to 330 degrees Fahrenheit.
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Line the baking sheets with Parchment Paper or a Sill Pad.
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Using an electric mixer, cream the butter with the sugars in a large bowl.
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Add the vanilla extract.
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Stir in the peanut butter.
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Add the eggs, one by one.
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Stir the baking powder into the flour. Then, gradually add the flour to the peanut butter batter.
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For easy handling, refrigerate the batter for 30 minutes.
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Roll the dough into 1-1/2 inch balls. Dip each ball into some of the extra sugar.
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Space the balls about 2-3 inches apart. I baked 9 cookies per baking sheet.
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Using a fork, make the traditional crosshatch design.
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Sprinkle some additional sugar on top of each cookie.
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Bake for about 17 to 18 minutes.
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Note: Allow the cookies to cool completely before removing from the baking sheet.