Preheat oven to 350°F. Generously grease muffin cups with butter.

In a medium bowl, whisk together flour, baking powder, salt, and nutmeg.

In a large bowl, use an electric mixer to beat together softened butter and sugar until light and fluffy. Blend in eggs until well incorporated.

Slowly mix in flour mixture, alternating with milk, until all ingredients are blended. Stir in vanilla.

Divide batter between muffin cups so that they are about ⅔ full. Bake until edges are starting to turn golden and a toothpick inserted in center comes clean, about 20 to 25 minutes.

While muffins are baking, pour melted butter in a bowl. Mix sugar and cinnamon together in another bowl.

As soon as muffins are done, allow them to cool for just a minute or two before turning them out of the pan.

Dip the top of each muffin in butter, allowing it to soak for about 10 seconds, and then press it into the cinnamon sugar mixture until generously coated. Serve warm.