Lightly grease two microwave-safe mugs with butter or cooking spray.
In a small bowl, whisk together the self-rising flour, cocoa powder, and a pinch of salt.
In another bowl, whisk the egg, milk, and vanilla extract until smooth.
Add the melted butter, brown sugar, and granulated sugar to the wet ingredients. Whisk until well combined.
Gradually add the dry ingredients to the wet mixture, stirring until a smooth batter forms.
Fold in the chocolate chips.
Divide the batter evenly between the prepared mugs, filling each only about halfway.
Sprinkle additional chocolate chips over the top.
Microwave each mug cake for about 1 minute, depending on the wattage of your microwave.
Check for doneness by inserting a toothpick into the center. If it comes out clean, the cake is ready. If needed, microwave for an additional 10–15 seconds.
Let the mug cake cool for 1–2 minutes before serving.
Enjoy warm on its own or top with powdered sugar, whipped cream, or vanilla ice cream.