Sift flour, baking powder, salt and baking soda into a medium bowl. Whisk to mix.
Place butter and sugar in a stand mixer with a paddle attachment. Beat at medium-high speed for 5 minutes until fluffy and light in colour. Scrape mixture down the sides and into the bowl. Add egg and vanilla. Continue beating for 3 minutes until light and fluffy again. Scrape down the sides of the mixing bowl. Continue to mix for 2 more minutes. Add sifted flour mixture and beat on low speed until incorporated. Scrape sides again. Add toffee bits and mix on low until incorporated.
Scoop out 2 tbsp of dough for large cookies or 1 tbsp for small cookies. Roll each into a ball and place on a baking sheet.
Refrigerate until cookies firm up, about 1 hour. Place in a resealable plastic bag and move to the freezer. Freeze for at least 8 hours. For best results, freeze for 24 hours. Frozen dough will keep well for up to 3 weeks.
When ready to bake, preheat oven to 350˚F. Line a baking sheet with parchment paper. Arrange cookies on the sheet, spacing them 2 inches apart.
Bake in centre of oven for 15 to 18 minutes until golden brown around edges. The cookie centres should still be soft. Let cool on the baking sheet for at least 15 minutes.