Preheat your oven to 400 degrees Fahrenheit.
In a large mixing bowl, cream together cubed cold butter, brown sugar, and regular sugar for about 3-4 minutes until light and fluffy.
Incorporate the eggs into your butter-sugar mixture and mix for an additional minute until smooth and creamy.
Gradually fold in dark unsweetened cocoa powder, all-purpose flour, cornstarch, baking soda, espresso powder if using, and salt until well combined.
Chop chocolate-covered toffee bars into chunks and fold them into your cookie dough along with semi-sweet chocolate chips if desired. Roll the dough into 6-ounce balls.
Place cookie dough balls on a parchment paper-lined baking sheet. Bake for about 9-11 minutes; press extra toffee chunks onto the tops before finishing baking. Let cool on the pan for at least ten minutes before transferring to a wire rack.