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 sugar on low speed until combined. Gradually increase the speed to medium-high and beat until light and fluffy, about 1 minute.

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, pinching the middle to resemble a peanut.

Place the dough on the prepared baking sheets, spacing them 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 around the edges but still soft in the middle. Remove from the oven and allow to cool completely.

While the cookies cool, make the filling. Combine the peanut butter, powdered sugar, 3 tablespoons of the heavy cream, and vanilla extract in a stand mixer fitted with the paddle attachment.

Beat on low speed until smooth. 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 of filling onto the bottom of one half and sandwich with another half. Repeat with the remaining cookies.