In a microwave-safe mug, combine the flour, granulated sugar, baking powder, and salt. Mix well.
Add the milk, vegetable oil, and vanilla extract to the dry ingredients. Stir until just combined.
In a small bowl, mix together the brown sugar and ground cinnamon. Drizzle the melted butter over the batter in the mug, then sprinkle the cinnamon-sugar mixture on top. Use a fork or toothpick to swirl the filling into the batter.
Microwave the mug on high for 1 minute and 30 seconds, or until the center is set. Cooking time may vary based on your microwave's wattage.
While the cinnamon roll is cooling, prepare the icing by whisking together the powdered sugar, milk, and vanilla extract until smooth.
Drizzle the icing over the warm cinnamon roll and enjoy!