Cream together the butter (still partially melted) sugar, and brown sugar for 2-3 minutes until it starts to get smooth. 1 cup brown sugar , 1/2 cup granulated sugar
Add in the eggs and vanilla extract and stir until just combined, when there is no longer any yellow steaks of the egg. 2 large eggs, 1/2 TBS vanilla extract
Add in the flour, baking soda, and salt. Stir until combined. 2 3/4 cups all purpose flour, 1 tsp baking soda , 1 tsp baking soda
Add in the Chocolate Chips, and about 2 cups of the toffee pieces (reserving the rest to place on top of the cookies after baking). 1 cup Semi Sweet Chocolate Chips
Cover the dough and place it in the fridge for 2 hours, up to 24 hours. If longer than about 12 hours, the dough may need to sit out for 20-30 minutes to be workable.
Preheat the oven to 350 degrees Fahrenheit. Line two cookie sheets with parchment paper, or silicone liners, and set them aside.
Scoop the dough by 3-4 TBS portions and roll them into balls.
Place 6 to 8 cookies on each cookie sheet.
Bake the cookies until the edges are golden brown, and the tops are just set, about 10-13 minutes. Bang the pan, a couple times half way through baking to help the cookies flatten a bit.
Remove the pan from the oven. Top each cookie with 2-3 pieces of toffee, and chocolate chips.
Let the cookies cool on the cookie sheet for 5 to 10 minutes, then transfer them to a cooling rack to continue cooling completely.