Brown the butter over medium heat, stirring constantly until the butter begins to foam and turns a golden brown, emitting a nutty aroma roughly 5–8 minutes. Scrape into a large bowl and let cool slightly for about 10 minutes.

In a large mixing bowl or stand mixer combine the cooled brown butter, brown sugar, and white sugar. Beat until mixed together. Add in the egg, egg yolk, and vanilla extract. Mix well.

Reduce mixer speed to low; add dry ingredients and beat just to combine. Mix in toffee pieces and chocolate wafers with a wooden spoon or rubber spatula. Fold in the chocolate. Do not over-mix!

Refrigerate the cookie dough for at least a half-hour, or overnight. Cookie dough can be made up to 3 days ahead. Just cover and chill. 

When you are ready to bake the cookies, preheat the oven to 350°F and line a cookie sheet with parchment paper. Use a cookie scoop to scoop the cookie dough out into balls, placing them 2 inches apart on the prepared sheet. 

Bake cookies until edges are golden brown and firm but centers are still soft, 9–11 minutes or, until the edges are just golden brown, and the centers have puffed up but are still gooey. Let cool on baking sheets for 10 minutes, then transfer to a wire rack and let cool completely.