In a large bowl with an electric hand-held mixer beat the butter, brown sugar, white sugar, and peanut butter until fluffy. Add the egg and vanilla and continue mixing.
In another medium-size bowl whisk together the flour, baking soda, and baking powder and add to the butter mixture. Turn the mixer on LOW and mix until just combined.
Chill the dough for 30 minutes in the refrigerator.
Preheat the oven to 375℉ and line 2 large baking sheets with parchment paper. Take dough out of the refrigerator and roll into balls (using about 1 ½ teaspoons of dough per cookie). Place 12 cookies on each pan and use your thumb or a round measuring spoon to make an indent in each dough ball.
Bake the cookies one pan at a time in the preheated oven for 9-10 minutes. Take the cookies out of the oven and use your measuring spoon to press the indent in again as they might have puffed up during baking. Let cookies cool for 2 minutes on the pan and then transfer to a wire rack to finish cooling.
When the cookies are fully cooled add the cooled ganache to a piping bag or a sandwich bag with the corner snipped off. Pipe about a teaspoon of ganache into each cookie's indent. Place the cookies in the refrigerator for the ganache to set up. Take the cookies out of the refrigerator 30 minutes before serving. Enjoy!
For the Ganache:
While the cookies are baking heat the whipping cream in a small saucepan over low heat until just under boiling. Add the chocolate chips and vanilla and let sit for 1 minute. Whisk mixture until ingredients come together and all the chocolate chips are melted. Let cool while the cookies cool.