In a large bowl, cream together butter, shortening, and both sugars with an electric mixer for about 3 minutes or until light and fluffy. Beat in your egg and vanilla until combined.
In a separate container, combine flour, baking soda, baking powder, and salt. With your mixer on low, slowly add your dry ingredients and beat until incorporated.
Fold in in your chocolate and toffee.
Scoop your cookie dough onto your baking sheet leaving about two inches in between. These cookies will spread quite a lot, so give them ample room. Bake for 9-10 minutes or until they just start to brown around the edges.
Let the cookies cool on the pan for about five minutes, and then remove the cookies to a cooling rack.