Mix butter, peanut butter, brown sugar, granulated sugar, egg, and vanilla extract with an electric mixer until creamy. Add in flour, baking soda, baking powder, and salt and mix until thoroughly combined. Cover and refrigerate the dough for 2 hours.
Preheat oven to 375 degrees F. Shape dough into 2” balls, and place 3” apart on ungreased baking sheets. Flatten the cookies with a fork in the traditional peanut butter cookies crisscross pattern, then bake in the pre-heated oven until the edges just start to become golden brown, about 9-10 minutes.
Remove from the oven and cool on baking sheet for 5 minutes before transferring to a wire rack to cool completely.
When the cookies have cooled completely, put some mini chocolate chips in one shallow bowl and chopped peanuts in another shallow bowl. Place a flattened scoop of vanilla ice cream between 2 cookies, then roll the edges in mini chocolate chips. Place a flattened scoop of chocolate ice cream between 2 cookies, then roll the edges in the chopped peanuts. Repeat with the rest of the cookies, and serve immediately.