Brown butter in a pan on medium high heat, stirring occasionally. Remove from heat and dissolve in instant coffee. Set aside and let cool.
Add granulated and brown sugar to the butter mixture followed by egg and vanilla extract. Cream together until smooth and glossy.
Combine salt, baking soda, flour and chopped chocolates and evenly fold into the butter mixture.
Form balls with the cookie dough and place them on a parchment or plastic-lined tray. Cover loosely and let rest in the fridge at least overnight or up to 3 days. The longer you refrigerate the less spread you'll get in the cookie when you bake it.
Preheat the oven to 325°F. Transfer the cookie dough to a parchment lined baking sheet and bake for about 18 minutes.
Sprinkle with sea salt and let cool.