Preheat the oven to 350°F. Line a large baking sheet with parchment paper.
Whisk together the flour, baking soda, baking powder and salt in a bowl and set aside.
In a large bowl using a stand mixer withe a paddle attachment or a hand mixer, beat the butter, granulated sugar, brown sugar until light and fluffy. Beat in the peanut butter until combined. Beat in the egg until combined completely ,then add in the vanilla.
Gradually add the flour mixture to the butter mixture, beating until well blended. Stir in the Reese's pieces.
Drop by heaping tablespoonfuls onto the prepared baking sheet.
Bake 10 to 12 minutes or until edges are lightly browned and the middle of the cookies is just set, then remove from the oven.
Cool on the baking sheet for 5 minutes then transfer to a baking rack to cool completely.
Store in a closed container at room temperature for up to 5 days or freezer for up to 3 months.