Preheat oven to 375 F. Line baking sheets with parchment paper or silicone baking mat.
Melt butter in a heavy saucepan.
Add brown sugar to a large bowl.
Pour melted butter over sugar.
Stir to combine butter and sugar. Let stand 5 minutes.
Add egg and egg yolk; stir to combine.
Stir in vanilla extract.
Add flour, baking soda, and salt. Stir until just combined.
Stir in toffee bits and chocolate chips.
I like to chill the dough for at least 30 minutes to give the ingredients a chance to meld.
Using a medium cookie scoop (1.5 tablespoon), drop scoops of dough 2 inches apart on prepared cookie sheet.
Bake for about 8-12 minutes, or until the edges of the cookies are golden brown.
Let cool on cookie sheet for 5 minutes. Remove to wire rack to finish cooling.
Be sure to avoid packing the flour when you measure. Weighing will give you the most accurate measurements. If you don't weigh the flour, you may find that you need to add less flour to avoid ending up with heavy cookies that don't spread.
I recommend mixing these cookies by hand to avoid over-mixing the dough.