Position oven racks in the top and bottom thirds of the oven and preheat to 350 degrees F. Line 2 baking sheets with parchment paper.
Beat the peanut butter, granulated sugar, brown sugar and salt with an electric mixer on medium-high speed in a large bowl until light and fluffy, about 5 minutes. Beat in the vanilla and egg. Fold in the chocolate.
Put some granulated sugar in a small bowl. Scoop tablespoonfuls of the cookie dough, roll them into balls and roll each ball in the sugar to coat. Evenly space them on the prepared baking sheets. Press each ball down with a fork to flatten it out and make an indentation.
Bake until the bottoms are golden brown, 10 to 12 minutes. Let the cookies cool for a few minutes on the baking sheets, then transfer to a rack to cool completely. The cookies can be stored in an airtight container at room temperature for up to 3 days.
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