In a microwave-safe mug, whisk together the flour, brown sugar, baking powder, cinnamon, and salt until combined. Add the milk, melted butter, and vanilla extract and stir until smooth. Fold in the diced apple.

Microwave on high for 1½–2 minutes, until the cake is set in the center. Let cool slightly.

In a small bowl, whisk together the cream cheese, powdered sugar, milk, and vanilla until smooth and spreadable. Spoon the frosting over the warm mug cake and serve immediately. Enjoy!