Preheat your oven to 350°F (175°C).
Line a 9x9 inch baking pan with parchment paper.
In a large mixing bowl, combine the softened unsalted butter and creamy peanut butter. Beat until smooth and creamy.
Add the granulated sugar and light brown sugar, and beat until light and fluffy, about 2-3 minutes.
Crack the egg into the bowl and mix until well combined.
In a separate bowl, whisk together the all-purpose flour, baking soda, baking powder, and salt. Gradually add this mixture to the wet ingredients, stirring until just combined.
Fold in 3/4 cup of the Reese's peanut butter chips into the batter, reserving 1/4 cup for topping.
Transfer the cookie batter to your prepared baking pan and spread it evenly.
Sprinkle the remaining peanut butter chips on top.
Bake for 20-25 minutes, or until the edges are golden and a toothpick comes out with a few moist crumbs.
Let cool in the pan for about 10 minutes, then lift out and cool completely on a wire rack before slicing.