Whisk together the flour, cocoa, baking soda, and salt. Set aside. In a separate mixing bowl, beat the butter and sugars together until smooth, about 2-3 minutes. Add the egg and vanilla and beat again.
Add the dry ingredients to the wet ingredients and beat again just until combined. Stir in the chocolate chips and toffee bits. Chill the dough 1 hour.
Preheat the oven to 375°F. Line a baking sheet with parchment paper or a silpat mat. Scoop the dough by tablespoons onto the baking sheet, leaving at least 2" in between the cookies. Return the remaining dough to the refrigerator in between batches.
Bake the cookies for 10 minutes, only until they begin to crisp on the edges and they look just a tiny bit gooey still in the center. Allow the cookies to cool on the baking sheet for at least 2-3 minutes before transferring to a wire rack to cool completely. Enjoy!