Preheat the oven to 350°F, set 2 of the oven racks to be as close to the center of the oven as possible, and line 2 standard baking sheets with parchment paper.
In a large bowl (or in the bowl of a stand mixer), add the butter, brown sugar, and cane sugar, and using an electric hand mixer (or the stand mixer), cream the butter and sugar on high for about 30-40 seconds.
Add the egg and peanut butter to the bowl with the creamed butter and sugar, and mix on high again until fully mixed.
Add the flour, baking powder, and salt. Mix on medium just until the dough comes together and thickens. If using, stir in the chocolate chips.
If you plan on rolling your cookies in cane sugar, go ahead and pour the cane sugar into a small bowl. Scoop the cookies and, if desired, roll them in the sugar, then place them on the pan at least one inch apart. You should have about 10-12 cookies per tray. Using a fork, press down on the cookies in a criss cross pattern -- the cookies should be about a ½-inch to ¾-inch thick.
Bake the cookies for 10-12 minutes. Swap their positions in the oven after 5 minutes (moving the bottom tray to the top and the top tray to the bottom). Remove them from the oven when the edges are golden brown, and allow them to cool completely before removing them from the pan, otherwise, they will crumble.
Enjoy!