Preheat the oven to 350 degrees F. Line your cookie sheets with parchment paper or silicone mats, then set aside.
In a medium bowl, whisk the flour, baking soda, and salt together, then set this aside.
In a large bowl, beat together the melted butter, peanut butter, brown sugar, and granulated sugar. Then beat in the egg and vanilla. Mix until these are well incorporated.
Add the flour mixture dry ingredients to the butter and peanut butter mixture. Use a wooden spoon to mix this until just combined. Do not over mix. Then stir the Reese’s pieces in
Then, shape the dough into 16 balls and smooth out using your hands. You can also use a cookie dough scoop.
Place the cookie dough balls on the prepared cookie sheets, leaving at least 2 inches of space between each one. Flatten each one just slightly with the bottom of a heavy glass.
Bake cookies for 10 minutes, then check them. We want the edges to be just barely be starting to turn golden, while the middle should still be soft. If they are not ready, keep baking but watch them closely. Take care not to over-bake, and remember that cookies do continue to bake on the baking sheet after you remove them from the oven.
Once they are done baking, take them out of the oven and place baking sheet on a wire baking rack. If desired you add more Reese's Pieces candies to the top of each cookie by slightly pressing them into the warm dough. You just need to do this quickly while the cookies are still hot.
Allow the cookies to stay on the pan and cool for at least 10 minutes. Then move them to a cooling rack.