Over medium heat, melt the butter, then whisk in the brown sugar and vanilla for 1 minute. Cook the sugar for 6-10 mins, whisking occasionally, until a thermometer reads 295°F/146°C and it has a melted peanut butter consistency. If at any point the toffee begins to separate, remove the pan from the heat and whisk vigorously until it comes back together. Then, pour the toffee onto the prepared baking sheet. Set aside to cool.

Cook the butter in a stainless steel pan over medium heat until it looks foamy, smells nutty, and has browned bits of milk solids. Scrape into a large bowl and cool to room temperature.

Once cool, whisk in the brown sugar and granulated sugar. Then, whisk in the egg, egg yolk, and vanilla until combined. Fold in the flour, baking soda, baking powder, salt, chocolate, and toffee pieces until just combined. Set the bowl aside for 15 minutes.

Scoop the dough with a large cookie scoop (3 tablespoons) and place them onto the prepared baking sheets, with 7-8 cookies on each tray. Make sure to press extra pieces of toffee and chocolate on top before baking! Then, bake the first tray of cookies for 10-13 minutes, or until the edges are golden brown but the centers are still soft and underbaked. Let the tray cool on a wire rack while you bake the second tray. After 10 minutes, use a spatula to transfer the cookies from the baking sheet to the rack to finish cooling. Press more pieces of toffee into the tops after baking for more crunch!