In a bowl whisk together the flour, baking powder, and salt.
In a stand mixer fitted with a paddle attachment, cream together the melted butter, sugar, brown sugar, and peanut butter until smooth. Beat in the egg. Add the flour mixture and mix until just combined. Using a 1-inch cookie/ice cream scoop, portion out the cookie dough and line them up on a baking sheet. They can be tightly packed, because you'll be refrigerating them. Once they are chilled you can easily move them apart onto multiple baking sheets. I do this with most of my cookie dough, then I toss the chilled balls of dough into a plastic bag and freeze them. It is a great way to have cookie dough at the ready for a fast onset craving.
Refrigerate the dough for at least a couple of hours or overnight. Once you are ready to bake, preheat the oven to 350°F. Line baking sheets with parchment and position the dough balls on the sheets so they have plenty of room to be smushed down.
Generously cover the dough balls with sugar.
Using a glass, smush the cookies until they are about 1/2-inch thick. If the dough is sticking to the glass add more sugar next time.
Make the crosshatch pattern with the tines of a fork. Bake for 9 to 10 minutes (or up to 12 if you like a crisper version).