Preheat the oven to 400° F with racks in the upper and lower thirds of the oven. Line two baking sheets with parchment paper and set aside.
In a large bowl, cream the butter and sugars on medium speed until light and fluffy, about 4 minutes.
Add the eggs, one at a time, beating well after each addition. Add the vanilla and mix to combine. Scrape down the sides and bottom of the bowl.
In a medium bowl, whisk together the flour, baking powder, baking soda, and salt. Add this to the butter mixture on low speed just until incorporated. Add the toffee bits and mix to combine.
Use a 2 tablespoon cookie scoop to scoop the dough onto the prepared baking sheets, making sure to space them very far apart as they will spread significantly. You should only fit about 5 cookies on one sheet tray.
Bake the cookies, rotating the sheets from top to bottom and banging the pans halfway through baking, about 10-12 minutes or until golden brown. Let cool on the baking sheet before transferring to a cooling rack to cool completely. Store cookies in an airtight glass container to keep them crisp.