Lightly grease a 12-16 ounce microwave-safe mug with butter or cooking spray. This prevents sticking and makes the cake easier to eat.
In the mug, whisk together the flour, granulated sugar, baking powder, and salt with a fork until no lumps remain.
Add the milk, oil, and vanilla extract to the dry ingredients. Stir with a spoon until just combined and smooth, about 15-20 strokes. Don't overmix.
In a small bowl, combine the brown sugar and cinnamon. Sprinkle this mixture evenly over the top of the batter.
Use a knife or skewer to swirl the cinnamon sugar through the batter in a figure-8 motion, dragging from bottom to top 3-4 times. You want ribbons, not full incorporation.
Microwave on high for 60-90 seconds, depending on your microwave wattage. The cake is done when the edges pull away from the mug and the center looks set but slightly glossy.
Let the cake rest in the microwave for 30 seconds to finish cooking with residual heat.
While the cake rests, whisk together the powdered sugar and milk in a small bowl until smooth. Drizzle over the warm cake and serve immediately.
