1. Preheat the oven to 350°F. Generously butter the muffin cups, ensuring they are well-coated.

Prepare the dry ingredients:

1. In a medium-sized bowl, whisk together the flour, baking powder, salt, and nutmeg.

Mix the wet ingredients:

1. In a large bowl, cream the softened butter and sugar using an electric mixer until the mixture becomes light and fluffy.
2. Beat in the eggs one at a time until fully incorporated.
3. Gradually add the dry ingredients, alternating with the milk, mixing just until everything is well combined.
4. Stir in the vanilla extract.

Fill the muffin cups:

1. Divide the batter evenly among the prepared muffin cups, filling each about two-thirds full.
2. Bake for 20 to 25 minutes, or until the edges begin to turn golden and a toothpick inserted into the center of a muffin comes out clean.

Prepare the coating:

1. While the muffins are baking, melt the butter in one bowl. In a separate bowl, mix together the sugar and cinnamon.

Coat the muffins:

1. As soon as the muffins are out of the oven, let them cool for just a minute or two before removing them from the pan.
2. Dip each muffin in the melted butter, then roll it in the cinnamon-sugar mixture until generously coated.
3. Serve warm and enjoy.