Preheat oven to 350 degrees Fahrenheit. Grease cookie sheets lightly or line them with nonstick baking mats.
In the bowl of an electric mixer, cream together butter, granulated sugar, brown sugar, egg and vanilla. Add flour, baking soda, cinnamon, salt and toffee chips and mix until combined.
Roll or scoop dough into 1 1/2" balls and place at least 2" apart on prepared cookie sheets. Bake for approximately 8 minutes. Don't over bake. Immediately after removing them from the oven, press additional toffee bits onto the tops of the cookies, if desired. Let sit on the cookie sheets for one or two minutes, then carefully remove cookies to a cooling rack to cool completely.