1 cup (2 sticks) unsalted butter, melted and cooled
1 cup light brown sugar, packed
3/4 cup granulated sugar for the dough, plus 1/2 cup granulated sugar for rolling
1 cup natural creamy peanut butter
2 large eggs, at room temperature
1 teaspoon vanilla extract
Line two baking sheets with parchment paper and set aside.
In a large bowl, whisk together the flour, baking powder, baking soda, cornstarch, and salt.
In a separate large bowl, use a hand mixer to cream together the cooled melted butter, the brown sugar, and 3/4 cup of granulated sugar until fully combined and slightly fluffy. Add the peanut butter, egg, and vanilla and mix until just evenly combined. Pour the flour mixture into the wet mixture and quickly mix until no clumps of flour remain. Make sure not to over-mix or your cookies will be puffy.
Roll the dough into 1/4 cup balls and roll them in the remaining granulated sugar. Place 6 cookie dough balls on each baking sheet, evenly spaced, and then gently press down on the tops with your palm to flatten slightly. Cover and refrigerate for 30 minutes. Preheat the oven to 350°F.
Uncover and bake the cookies for 12 minutes, or until just set around the edges but very soft and puffy in the middle. Allow the cookies to cool on the baking sheet fully without disturbing them to finish setting. Repeat with any remaining dough.