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

Place the butter in a small saucepan and set over medium-low heat. Stir and scrape the butter every 10 to 15 seconds until it turns golden brown, about 10 to 15 minutes.

Add the cocoa powder and vanilla to the brown butter and whisk to combine until no lumps of cocoa remain.

In a stand mixer, beat the eggs and brown sugar together until light, fluffy, and pale in color.

Add the butter mixture to the egg mixture and fold together with a rubber spatula.

Add the flour and salt, and fold until no streaks of flour remain. Fold in the chocolate chips, if using.

Transfer the mixture into the prepared baking pan and bake for roughly 25 minutes, testing for doneness starting at 20 minutes.