First, make the cookies. Preheat the oven to 350°F. Line a baking sheet with parchment paper. Set aside.
In a stand mixer fitted with the paddle attachment, beat together the peanut butter, butter and brown on low speed until combined. Gradually increase the speed to medium-high and beat until light and fluffy, about 1 minute. Use a silicone spatula to scrape down the sides and bottom of the bowl, then add in the egg and vanilla. Beat to combine.
Add the flour, cornstarch, baking soda, and salt and beat on low speed until just combined and no streaks of flour remain.
Use a 1 ounce cookie scoop to portion out equal amounts of dough. Shape the dough balls into flat oval discs, using your fingers to pinch the middle in so that each one looks like a peanut. Place the dough on the prepared baking sheets, spacing the dough 2 inches apart. Use a fork to make crosshatches on each circular end of the dough.
Bake for 9 to 10 minutes or until the cookies have puffed up and are set and firm around the edges but still somewhat soft in the middle*. Remove the baking sheet from the oven and allow the cookies to cool completely.
While the cookies cool make the filling. In a stand mixer fitted with the paddle attachment, combine the peanut butter, powdered sugar, 3 tablespoons of the heavy cream, and vanilla extract. Beat on low speed until smooth–do not over mix or the cream can split! If the filling feels too thick add the last tablespoon of cream. Transfer to a piping bag.
Match up the cooled cookies into pairs. Pipe about two teaspoons worth of filling onto the bottom of one half and sandwich together with the other half. Repeat with the remaining cookies. Enjoy!