Preheat the oven to 350 degrees F. Line 2 baking sheets with parchment paper.

Place the butter and sugars in a large mixer bowl and beat until smooth and creamy, about 3 minutes. Add the egg, egg yolk and vanilla and beat until incorporated. Scrape down the sides of the bowl. With the mixer on low, add the flour, baking powder and salt; beat well and scrape again. Stir in the chocolate chips and the toffee.

Divide the dough into quarters. Roll each quarter of the dough between two floured sheets of waxed paper into an 8-inch or so square. Transfer the cookie squares to the prepared baking sheets. Bake until lightly browned, 15 to 17 minutes.

While hot, cut each cookie square in half, then cut each half into eight 1-inch slices. Cool the slices on the cookie sheets completely.