In a bowl, combine flour, sugar, baking powder, salt, and nutmeg. In another bowl, whisk together milk, egg, melted butter, and vanilla.
Pour wet ingredients into dry ingredients and stir until just combined and smooth.
Grease four 4-oz ramekins or small donut-shaped silicone molds. Fill each about two-thirds full with batter.
Preheat air fryer to 340°F. Place filled ramekins in the basket and cook for 10-12 minutes until golden and a toothpick comes out clean.
Let cakes cool for 3 minutes, then remove from ramekins. While still warm, brush each cake all over with melted butter.
Mix cinnamon and sugar in a shallow bowl. Roll each buttered cake in the cinnamon sugar mixture until completely coated. Serve warm.