Prep mug: Lightly grease the inside of a 12-ounce microwave-safe mug with butter or cooking spray.
Mix dry ingredients: In the greased mug, combine flour, granulated sugar, baking powder, and salt. Stir with a fork until evenly mixed.
Add wet ingredients: Add milk, melted butter, and vanilla extract to the mug. Stir gently with the fork until just combined into a smooth batter, about 15-20 seconds. Don't overmix.
Make cinnamon swirl: In a small bowl, mix together brown sugar, cinnamon, and melted butter until it forms a paste. Drop spoonfuls of this mixture on top of the batter in the mug.
Create swirl: Use a toothpick or knife to swirl the cinnamon mixture into the batter with figure-8 motions. Don't mix completely—you want visible ribbons.
Microwave: Place mug in the center of the microwave. Cook on HIGH for 70-90 seconds (start with 70 seconds for 1000+ watt microwaves). The top should look set and slightly firm when done.
Make glaze: While the cake cools slightly (1-2 minutes), whisk together powdered sugar, milk, and vanilla in a small bowl until smooth.
Finish and serve: Drizzle glaze over the warm mug cake. Eat immediately with a spoon, straight from the mug!