Preheat the oven to 350 degrees F (175 degrees C). Grease 12 muffin cups or line with paper muffin liners.

Stir flour, 1/2 cup sugar, baking powder, nutmeg, and salt together in a medium bowl. Make a well in the center.

Stir egg, milk, and 1/3 cup melted butter together in a separate bowl. Pour into the flour mixture; stir until just moistened. Batter may be lumpy. Spoon batter into the prepared muffin cups.

Bake in preheated oven for 20 to 25 minutes. Meanwhile, combine remaining 1/4 cup sugar and cinnamon in a small bowl while muffins are baking.

Dip tops of baked muffins in remaining 1/3 cup melted butter, then in the cinnamon-sugar mixture. Serve warm.