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 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 into flat oval discs and place on the prepared baking sheets, spacing 2 inches apart. Use a fork to make crosshatches on each cookie.

Bake for 9 to 10 minutes or until the cookies are puffed up and firm around the edges but still soft in the middle. Allow to cool completely.

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, without overmixing.

If the filling is too thick, add the last tablespoon of cream. Transfer to a piping bag.

Match up cooled cookies into pairs, pipe about two teaspoons of filling onto the bottom of one half, and sandwich with the other half. Repeat until finished.