Add butter to large microwave safe bowl. Microwave to melt butter almost completely in 30 second increments. Whisk to melt any remaining butter pieces.
Add sugars to melted butter.
Break up any chunks of brown sugar with whisk.
Whisk mixture vigorously to blend and help dissolve sugars.
It will gradually lighten in color and hold its shape. This make take a minute or so.
Add eggs and vanilla to butter/sugar mixture.
Whisk to fully incorporate all the egg whites, which tend to be sneaky and try to hide from you on the bottom of the bowl! Set mixture aside.
In small bowl, combine flour, baking soda, and salt. Use a wooden spoon to add to butter/sugar mixture.
Stir just unit all flour is blended. Scrape down sides of the bowl.
Stir in chocolate covered toffee pieces and chocolate chips.
Chill dough in refrigerator for about 15 minutes while you preheat oven to 375 degrees and prepare baking sheet by lining with parchment paper.
Roll dough into 1.5 inch balls and place about 2 inches apart on cookie sheet.
Bake about 10 minutes or until set.
Cool on baking sheet about 5 minutes. Remove to cooling rack to cool completely. Store in airtight container.