Brown Butter: Cook butter on medium-low heat. Stir often until butter melts, bubbles & foams. Stir often until there are lots of brown flecks & it smells like toffee, but not burnt. Pour in a bowl to stop cooking & let it cool. It should be melted, but not warm to touch.
Whisk Dry Ingredients: While brown butter cools, whisk together dry ingredients. In a small bowl add flour, baking soda and salt. Lightly whisk and set aside.
Make Cookie Dough: Add cooled, browned butter, & sugars to large mixing bowl or bowl of standing mixer. Beat (with mixer or hand mixer) butter & sugars together for 30 seconds or so, then add egg & vanilla. beat on medium high until combined. Add dry ingredients & beat on low until almost combined. Finish the dough by scraping sides and folding remaining flour in - as to not over mix. Add chocolate chips and toffee pieces & fold (if skipping toffee, add extra chocolate!).
Scoop Cookie Dough: Using a 2.5-3tbs cookie scoop, scoop cookies. Gently roll them into a smooth ball. Place them on baking sheet or try to chill. Chill uncovered 1-2 hours (30 minutes bare minimum, but best at 1.5-2 hours).
Preheat Oven to 350°: With 10 minutes left of chill time, preheat oven to 350*. If dough chilled overnight, let it sit out on countertop while oven preheats to warm up a bit.
Bake Cookies: On a cookie sheet lined with parchment or silpat, place cookies about 2 inches apart. Lightly press a few more chocolate chunks or toffee pieces on top. Bake 11-12 minutes or until cookie is golden brown on the bottom. It may take 10 minutes or up to 14 minutes depending on your oven. They should be lightly golden on the bottom edges, and puffed. They will collapse and crinkle to perfection as they cool.
Let cool 5 minutes on baking sheet before moving to wire rack to finish cooling.