Combine butter, peanut butter, and brown sugar and ¼ cup granulated sugar in a large bowl (or in the bowl of a stand mixer) and use an electric mixer to beat until creamy and well combined.
Add egg and vanilla extract and stir until well-combined.
In a separate bowl, whisk together flour, cornstarch, baking soda, and salt.
Gradually stir the flour mixture into the peanut butter mixture. Make sure to pause periodically to scrape the sides and bottom of the bowl to ensure all ingredients are well-combined.
Cover mixing bowl with plastic wrap and place peanut butter cookie dough in the refrigerator to chill for 30 minutes to one hour (start with 30 minutes, if the dough is too sticky or your cookies are coming out of the oven too flat, chill for an additional half an hour. This dough may be chilled overnight if you'd like).
Preheat oven to 350F (175C) and line baking sheets with parchment paper.
Once dough has chilled, remove from refrigerator and scoop into heaping 1 ½ Tablespoon-sized balls.
Roll the cookie dough between your palms until smooth and then roll thoroughly in additional granulated sugar. Place on prepared cookie sheet, spacing cookies at least 2" apart.
Use the tines of a fork to gently make a criss-cross pattern on the surface of each cookie by slightly pressing down.
Bake on 350F (175C) for 9-12 minutes. Edges should be just turning golden brown but the cookie centers should appear slightly under-baked, allow cookies to cool completely on the cookie sheets and the centers will finish baking (but remain soft and chewy) as they cool on the cookie sheet. Don't over-bake or the cookies will be dry.
Allow peanut butter cookies to cool completely on baking sheet before enjoying.
¹I do not recommend using a natural peanut butter (the kind where the oil separates that you have to stir)Please note that the recipe video states to bake the cookie dough on 375F for 8-11 minutes. This will work, but recently I've found that baking on a slightly lower temperature (350F) for a minute longer makes the cookies even softer and so that is now what I recommend.This cookie dough freezes well. Chill the dough as instructed then scoop and roll through sugar before freezing in an airtight container. Cookie dough will still need to bake on 375F but may need an additional minute or so in the oven.