Preheat oven to 375°. Coat a standard 12-cup muffin pan with nonstick spray. Whisk flour, baking powder, salt, and nutmeg in a medium bowl; set aside.
Using an electric mixer, beat butter and sugar in a large bowl until light and fluffy, about 4 minutes. Beat in egg. With mixer on low speed, add dry ingredients in 3 additions alternating with milk in 2 additions, beginning and ending with dry ingredients.
Divide batter among muffin cups and bake, rotating pan halfway through, until a tester inserted into center comes out clean, 30–35 minutes. Let cool 5 minutes in pan, then transfer to a wire rack.
Mix sugar and cinnamon in a medium bowl. Working one at a time, dip muffins in melted butter, then coat with cinnamon sugar mixture.