Brown the butter in a small saucepan at medium heat, 6-8 minutes. Place the browned butter in the fridge for 5 minutes. Then move it to the freezer for 10 minutes.
In a large mixing bowl combine the now cooled browned butter, brown sugar, and granulated sugar.
Add the egg, egg yolk, and vanilla extract and combine. Add the baking powder, baking soda, and salt and combine.
Add the flour and espresso powder and combine. Add the chopped bittersweet chocolate and combine.
Shape the cookies into round balls using 2 tablespoons of dough per cookie, placing 9-12 cookies per baking sheet.
Bake for 8-9 minutes. Remove the cookies from the oven and immediately sprinkle with flaky sea salt (if using).
Notes
Espresso Powder: This can be purchased from King Arthur Baking Company via Amazon. If you plan ahead a couple of days, this is the easiest approach (rather than using ground espresso).
Chocolate: I recommend bittersweet chocolate bars, chopped into chunks, but semi-sweet, dark, or milk chocolate would all work well. Use high quality chocolate, like Guittard or Ghirardelli.
Flaky Sea Salt: This is optional but adds such a nice touch. I use Morton’s Sea Salt Flakes. It’s expensive but one box will last you at least a year if not significantly more.
Presentation: If you have extra chocolate chunks, either in the bottom of the bowl, or if you want to cut up more, you can press them into the tops of the cookies. They will melt into the top of the cookies when baked for a melty chocolatey mouthwatering appearance.
I find that it's best to press a few smaller pieces into the top edges/sides of the cookies for a more natural look. One piece of chocolate in the center of the cookie always looks a little off to me.
Test Cookie: I always recommend making a test cookie before tossing a whole baking sheet worth of cookies in the oven, especially when trying a new recipe. A test cookie will tell you if your cookie dough temperature is too warm (if so stick it in the fridge for 20-30 min) or if you need to increase or reduce the baking time by 1-2 minutes.
Don't Overmix: Overmixing the dough can develop the gluten in the flour making the cookies tough (think like pizza crust), rather than soft and chewy.