Position a rack in the center of the oven and preheat to 350 degrees F. Line a 18-by-13-inch baking sheet with parchment.
Whisk together the flour, baking powder and salt in a medium bowl.
Beat the butter and 2 cups of the sugar together in a large bowl with an electric mixer on medium speed until light and fluffy, scraping down the bowl as needed. Add the eggs, peanut butter and vanilla and beat until smooth and creamy. Gradually add the flour mixture, mixing until the dough comes together and is smooth.
Turn the dough out onto the prepared baking sheet. Form into a ball, cover with plastic wrap and chill about 40 minutes.
Roll the chilled dough ball in the remaining 1/4 cup of sugar. Put the cookie back on the baking sheet and bake for 15 minutes. Reduce the temperature to 300 degrees F and bake, rotating the pan half way through, until golden brown and the center is set, but still soft, about 1 hour to 1 hour 10 minutes more. Cool on the pan on a wire rack for 5 minutes. Push the chocolate kiss-shaped candy into the center of the cookie. Cool another 40 minutes before slicing into wedges and serving.
When measuring flour, we spoon it into a dry measuring cup and level off excess. (Scooping directly from the bag compacts the flour, resulting in dry baked goods.)
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