Preheat oven to 400° F. Prepare two baking sheets by lining with either parchment paper or a silpat liner.
In small bowl, mix flour, baking soda, and salt.
In stand mixer, cream butter and brown sugar on medium speed until light and fluffy, about 2-3 minutes. Add vanilla and egg, mixing well. Add flour mixture, and mix slowly to incorporate, then beat to blend well for the least amount it takes to fully incorporate the ingredients. Stir in chocolate chips and toffee pieces.
Drop batter in 2-tablespoon portions about 2 inches apart on baking sheets.
Bake in a 400° oven until edges of cookies are brown but an area about 1 inch wide in the center is still pale, 7-12 minutes.
Let cookies cool on pan about 5 minutes, then transfer to cooling racks with a spatula. Serve warm or cool. Store in an airtight container or freeze for longer storage.