Preheat your oven to 350°F. Grease and line an 8 x 8-inch pan with parchment paper on all sides. Set aside.

Place the butter in a small saucepan over medium-low heat. It's important to keep the heat low for even browning. Use a silicone spatula to stir and scrape the butter from the bottom and sides of the pan every 10 to 15 seconds. Initially, the butter will melt and foam. As it cooks, the foam bubbles will decrease in size, and the butter will develop a warm, nutty aroma. Continue cooking and stirring occasionally with the spatula until the butter turns golden brown and you notice small browned bits floating, about 10 to 15 minutes. These are the milk solids in the butter toasting. Remove the butter from the heat once it reaches a golden brown color.

Add the cocoa powder and coffee to the browned butter. Whisk until well combined and no cocoa lumps remain.

With a handheld beater, beat the eggs and brown sugar together until the mixture becomes light, fluffy, and pale in color.

Pour the brown butter mixture into the egg mixture and use a rubber spatula to fold them together.

Sift in the flour and add salt to the batter. Fold gently using a rubber spatula until no streaks of flour are visible. Finally, fold in the chocolate chips if desired.

Transfer the batter into the prepared baking pan. Bake for approximately 25 minutes, starting to check for doneness at 20 minutes. The edges should be set, but a knife inserted into the center should still come out with some batter on it. Depending on your oven, baking time may range up to 35 minutes.