Preheat oven to 350 degrees. Line 2 baking sheets with silicone baking mats or parchment paper and set aside.
Cream butters and sugars together until light and fluffy. Stir in egg and vanilla. Scrape sides and mix again. Incorporate baking soda and flour until just combined. Stir in toffee bits by hand.
Scoop 8 dough balls onto baking sheet leaving lots of room around each cookie to expand. Press down cookie dough balls using a fork. Bake 7-8 minutes. Cool on baking sheet 3 minutes and then remove to cooling rack. Serve immediately or store in airtight containers for up to 3 days.