First make the brown butter. Cut the butter into tablespoon pieces. In a small bot or saucepan heat the butter over medium to high heat for 7-8 minutes. Use a rubber spatula to stir it now and again so it heats evenly. The butter will foam some. Once you see small bits of brown and the butter smells very nutty (almost like caramel or toffee nut) remove from heat. Allow to cool to room temperature or close before using.
In a large mixing bowl add the cooled butter and sugars. Cream together. Then stir in the vanilla extract and egg.
In a smaller bowl combine the flour, salt and baking powder. Whisk together.
Then add this dry mixture to the wet mixture and stir to make the dough.
Last add the chocolate chips. Refrigerate the dough for at least an hour to overnight before baking. I like to go ahead scoop all the dough into cookies before refrigerating, I will sometimes put half in the freezer (espeically if I make a double batch).
If using flaky sea salt add it to the tops of dough balls before baking. Bake at 350°F for 10-12 minutes. I tend to bake for 12 minutes but I usually check them after 10.
Notes
You can use unsalted butter or salted butter to make brown butter. For this recipe (and most baked goods) I tend to use unsalted butter.
Brown butter will not all turn brown, it will have small brown flecks in it. What browns in the milk solids, not the entire mixture. It can go from brown to burnt pretty quickly, so keep it an eye on it.
Crack the egg in a separate, small bowl before adding to the batter. This way if you see some shell go in you can remove it (with a larger piece of shell) before adding to the batter.
Chocolate chips are great but you could also use chopped chocolate or substitute other chips like peanut butter chips, white chocolate chips, toffee chips, etc.