Step 1: In a small microwave-safe mug (10-12 oz capacity) or a small ramekin, melt the unsalted butter in the microwave for about 30 seconds. Swirl to ensure it's fully melted.
Step 2: To the melted butter, add the granulated sugar, egg yolk, and vanilla extract. Whisk thoroughly with a fork until well combined and smooth.
Step 3: Add the all-purpose flour, unsweetened cocoa powder, baking powder, salt, and optional instant espresso powder to the wet mixture. Mix until just combined. Do not overmix; a few small lumps are okay.
Step 4: Stir in the milk until the batter is smooth and well incorporated. Finally, fold in the 3 tablespoons of mini chocolate chips.
Step 5: Sprinkle a few extra mini chocolate chips on top of the batter in the mug.
Step 6: Microwave on high for 60-90 seconds. Cooking times can vary based on microwave wattage. Start with 60 seconds and microwave in 10-second increments until the cake is set on the edges but still looks slightly moist in the center (it will continue to cook slightly as it cools).
Step 7: Carefully remove the mug from the microwave (it will be hot!). Let it cool for a minute or two before digging in. Serve warm, perhaps with a scoop of ice cream or a dollop of whipped cream, and enjoy your Homemade Single-Serve Chocolate Dot Cake!