Preheat the oven to 350°F. In a large mixing bowl, cream together the softened butter and sugar.
Add the egg and vanilla. Beat at medium speed until the mixture is combined, scraping the bowl often.
Add the flour, baking powder, and baking soda. Reduce the speed to low and beat just until no visible streaks of flour remain. Mix in the English toffee bits.
Shape the dough into 1 ¼ inch balls and place them on a parchment-lined baking sheet about 2 inches apart. Flatten the cookies with the bottom of a glass.
Sprinkle more toffee bits on top.
Bake the cookies for 9-12 minutes, or until the edges are lightly browned (do not over-bake). Allow the cookies to cool for a few minutes before transferring them to a wire rack to cool completely. Enjoy!