Preheat your oven to 300°F. Line a cookie sheet with parchment paper or a silicone liner.
In a mixing bowl, cream together the softened butter, peanut butter, brown sugar, and granulated sugar until light and fluffy.
Add the egg and vanilla to the mixture, and mix until well combined.
Incorporate the all-purpose flour, cornstarch, baking soda, and salt into the mixture. Mix until a sticky dough forms.
Use a 2 tsp cookie scoop to portion out the dough onto the prepared cookie sheet. If you don't have a cookie scoop, refrigerate the dough for 15-20 minutes for easier handling.
Bake the cookies at 300°F for 15-17 minutes, or until they flatten and the edges turn golden brown.
Once baked, let the cookies cool completely on the pan.
While the cookies cool, prepare the peanut butter filling:
- In a bowl, combine the peanut butter and softened butter until smooth.
- Add the powdered sugar and mix until thick.
- Gradually add the heavy whipping cream until a thick, creamy consistency is achieved.
Assemble the cookies by spreading or piping the peanut butter filling onto the bottom of one cookie and sandwiching it with another.
Repeat the process to make all the nutter butter sandwich cookies.
Store the cookies in an airtight container for up to 4 days.