Prepare the mug and dry ingredients. Choose a microwave-safe mug that holds at least 12 ounces. In it, combine the flour, granulated sugar, baking powder, ¼ teaspoon cinnamon, and salt with a fork until well mixed.
Add wet ingredients to form the batter. Pour in the milk, oil, and vanilla extract. Stir with your fork until the batter is smooth with no flour pockets. Make sure to scrape the bottom and sides of the mug.
Create the cinnamon swirl mixture. In a separate small bowl, combine the melted butter, brown sugar, and ½ teaspoon cinnamon. Stir until it forms a thick, syrupy paste.
Add the cinnamon swirl to the batter. Spoon the cinnamon mixture on top of your cake batter, then use a knife or toothpick to gently swirl it throughout the batter. Don’t overmix—you want distinct ribbons of cinnamon.
Microwave the cake. Place the mug in the microwave and cook on high for 60-70 seconds. The cake should be set but still slightly moist on top. If it looks too wet, microwave for additional 10-second intervals.
Prepare the cream cheese glaze. While the cake cools slightly, mix the softened cream cheese, powdered sugar, and vanilla in a small bowl. Add a few drops of milk if needed to reach a pourable consistency.
Finish and serve immediately. Pour the glaze over the warm cake and enjoy while still warm, when the texture and flavors are at their best.