Preheat your oven to 350°F and line two baking sheets with parchment paper.
In a large mixing bowl, use an electric mixer to beat the butter, brown sugar, and granulated sugar together until light and fluffy, about 2-3 minutes.
Add the egg, egg yolk, and vanilla extract to the bowl. Mix until fully incorporated.
Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined. Be careful not to overmix.
Fold in the chopped chocolate and pieces of the prepared toffee until evenly distributed throughout the dough.
Scoop about 2 tablespoons of cookie dough for each cookie, rolling them into balls. Place them on the prepared baking sheets, leaving about 2 inches of space between each cookie.
Bake the cookies for 10-12 minutes, or until the edges are set but the centers are still soft. The cookies will continue to bake on the hot baking sheet after they come out of the oven.