Preheat your oven to 415 degrees and prepare a baking sheet with parchment paper
In a medium bowl, whisk together flours, cornstarch, baking soda, and salt. Set aside.
Cut butter into small cubed pieces.
In a stand mixer fitted with a paddle attachment, combine butter, sugar and brown sugar until light and creamy (about 4-5 minutes).
Add vanilla extract and eggs. Mix until combined.
Add dry ingredients. Mix until just combined to avoid over mixing.
Stir in chocolate chips and 11/4 cups of toffee. Set remaining 1/4 cup of toffee aside to use for the topping.
Divide the dough in half. Use half of the dough to make 4 giant dollops of dough on the prepared cookie sheet.
Bake for 9-12 minutes or until golden brown at the edges.
Sprinkle toffee on the top of warm cookies.
Let the cookies rest on the baking sheet for at least 10 minutes.