Cream butter, brown sugar and sugar together until fluffy, about 2 minutes. Add in the egg and vanilla, mix well until fully incorporated. Add flour, cornstarch, baking soda, and salt, mix until just combined. . Fold in the chocolate chips.
Scoop balls of dough onto a baking sheet (about 2 Tablespoons per cookie) and chill for 30 minutes. Top the balls of dough with additional chocolate chips if desired.
Preheat oven to 350º F.
Bake cookies for 10-12 minutes, until the edges are set, the tops appear dry, and they are lightly golden. Remove from the oven and allow to cool on the baking sheet for a few minutes before removing to a wire rack to cool completely.
Cookie Dough Filling
Heat treat your flour by microwaving in a bowl for 30 second intervals, stirring after each time, until the flour reaches 160º F. You can also bake at 300º with the flour spread in an even layer for about 10 minutes, until it reaches 160º F. Let cool.
Beat together the butter and brown sugar together over medium speed until fluffy, 2-3 minutes. Add flour, powdered sugar, and salt. Mix on low until fully incorporated. Slowly add the heavy cream and vanilla. Beat for about 2 minutes, until fluffy. Stir in chocolate chips.
Assemble
Once the cookies are completely cool sandwich 1 rounded tablespoon of filling between 2 cookies. Gently press together until the filling spreads to the edges.
Store in an airtight container in the fridge. Let them set at room temperature for a few minutes before serving.