Position racks in the upper and lower thirds of the oven; preheat to 350 degrees F. Whisk the flour, baking soda, baking powder and salt in a medium bowl. Beat the butter, brown sugar and peanut butter in a large bowl with a mixer on medium speed until creamy, about 1 minute. Increase the speed to medium high and beat until fluffy, about 2 more minutes. Add the egg and vanilla and beat until combined. Reduce the mixer speed to low; add the flour mixture and beat until well blended. Add the chocolate chips and beat until combined.
Put the granulated sugar and confectioners¿ sugar in separate small bowls. Roll tablespoonfuls of dough into balls, then roll first in the granulated sugar and then generously in the confectioners' sugar. Arrange 2 inches apart on 2 ungreased baking sheets.
Bake, switching the pans halfway through, until the cookies are just firm around the edges and cracked on top, 15 to 18 minutes. Let cool 3 minutes on the baking sheets, then transfer to racks to cool completely. Dust the cookies with more confectioners' sugar, if desired.