In a small saucepan over medium heat, melt the unsalted butter. Continue cooking, stirring frequently, until the butter turns a deep golden brown color and emits a nutty aroma. Remove from heat and let the browned butter cool for a few minutes.

In a medium-sized mixing bowl, whisk together the all-purpose flour, baking powder, baking soda, and salt. Set aside.

In a large mixing bowl or using a stand mixer, mix the browned butter, brown sugar, and white sugar until well combined and creamy.

Add the crunchy peanut butter to the butter-sugar mixture and mix until fully combined. Then, add the egg and continue mixing until the batter is well blended.

Gradually add the dry ingredients (flour, baking powder, baking soda, and salt) to the wet mixture. Mix until just combined. Be careful not to overmix the dough.

Cover the cookie dough with plastic wrap and refrigerate for at least 30 minutes. Chilling the dough helps prevent the cookies from spreading too much while baking.

Once the dough has chilled, take it out of the refrigerator. Scoop about a tablespoon of dough and roll it into a ball between your palms.

Arrange the cookie dough balls on the prepared baking sheet, leaving enough space between each cookie to allow for spreading.

Use the back of a fork to gently press down on each cookie, creating a crisscross pattern. This also helps flatten the cookies slightly.

Place the baking sheet in the preheated oven and bake for 10 to 12 minutes or until the edges are lightly golden. The centers may still look slightly undercooked, but they will firm up as the cookies cool.