Preheat oven to 350F/180C degrees. Grease a 9-inch pie dish or cake pan. Set aside.
In a medium bowl whisk together flour, cornstarch, baking soda and salt. Set aside.
To brown the butter, place butter in a medium, heavy-bottomed saucepan over medium heat and melt. Keep heating just until small golden bits start to appear at the bottom, and the butter smells nutty and caramely. Watch it carefully because the butter can burn quickly at this point. Remove from the heat and immediately pour melted butter into a large bowl and allow it to cool slightly.
Add brown sugar and granulated sugar and whisk until well blended. Add egg and vanilla extract and whisk until combined. Stir in flour mixture, mixing just until combined. Don’t over mix. Fold in chocolate chips.
Press cookie dough into the pan. Bake for 20-25 minutes (mine is ready in 20-22 minutes) until deep golden brown but still soft at the center, covering it loosely with aluminium foil after 15 minutes so the edges won't brown too much. Remove cake from oven and set the pan on a wire rack. Allow to cool completely (I recommend then placing it in the refrigerator for a little while to set before slicing). Serve warm or at room temperature, with whipped cream or chocolate frosting, if you like.
Cake is best eaten the same day it's made but will keep, covered tightly, for up to 2 days at room temperature or in the fridge. Leftovers can be frozen for up to 2 months.