Preheat the oven to 175°C.
Prepare a muffin tin by greasing it lightly or lining with paper cases. In a mixing bowl, combine the flour, sugar, baking powder, salt, and nutmeg, whisking until well blended.
In a separate bowl, whisk together the milk, beaten egg, melted butter, and vanilla extract until smooth. Pour the wet mixture into the dry ingredients and gently stir until just combined; the batter should remain slightly lumpy to ensure tenderness.
Spoon the batter evenly into the muffin cups, filling each about two-thirds full. Bake for 20–25 minutes, or until a toothpick inserted in the center emerges clean. While the muffins are baking, combine the sugar and ground cinnamon for the topping in a small bowl.
Once baked, remove the muffins from the tin while warm. Dip the tops of each muffin first into the melted butter, then coat generously with the cinnamon sugar mixture.
Serve warm or allow to cool to room temperature.