Grease a large ramekin (ours was 14 ounces) or microwave-safe mug with baking spray or butter.
Put 3 tablespoons of unsalted butter in a large mug. Melt in the microwave for about 20 seconds until completely melted, then stir in 3 tablespoons of cocoa powder with a rubber spatula until smooth. Set aside to cool. In a separate small bowl, whisk the egg.
Once the butter and cocoa powder mixture is cooled off, add in whisked egg, milk, and ½ teaspoon of vanilla extract. Stir until you get a nice, smooth batter.
Add in 3 tablespoons of flour, 3 tablespoons of brown sugar, ¼ teaspoon of kosher salt, and ¾ teaspoon of baking powder. Stir until the batter is combined completely, but don't mix it too much, just until it's combined. Add the chocolate squares to the top.
Pop it into the microwave at full power for about 50 seconds to 1 minute and 20 seconds. This can vary a lot depending on the wattage power of your microwave, so just keep a close eye on it. Start with 50 seconds, then check the cake. Microwave in 5 to 10-second increments until set. The top should still be a little sticky, but fully set. It may rise out of the mug a little bit, but will deflate as it cools.
Dig in an enjoy right away while the cake is warm and the center is melty. Serve with vanilla ice cream, chocolate sauce, fresh berries, whipped cream, or whatever you like. Enjoy!