Preheat the oven to 350°F. Lightly grease a baking sheet and set aside.
Melt the butter in a medium skillet over medium heat. Cook for 4-5 minutes on medium heat, or until the butter gets foamy and starts to turn brown. Remove the butter from the heat and let it cool for 15 minutes.
In a stand mixer (or with a hand mixer in a large bowl), cream cooled browned butter, granulated sugar, brown sugar and vanilla for a few minutes. Add eggs and beat until fluffy (a few more minutes).
In a medium bowl, add flour, baking soda, baking powder and salt. Add dry ingredients and mix until combined.
Fold in toffee bits and chocolate chips. Use a medium cookie scoop to scoop dough, and roll into balls. Place onto the prepared baking sheet and top dough balls with extra chocolate chips.
Bake for 9–11 minutes.
While still warm, use the back end of a metal spatula to round out the cookies and add any more chips needed. Sprinkle on flaky sea salt if desired. Let cookies sit on the cookie sheet for a few minutes, then remove to a rack to cool.