Preheat oven to 350°F (175°C). Generously grease muffin cups with butter or nonstick spray.

Mix dry ingredients:
In a medium bowl, whisk together flour, baking powder, salt, and nutmeg.

Cream butter & sugar:
In a large bowl, beat softened butter and sugar with an electric mixer until light and fluffy. Add eggs and mix well.

Combine wet & dry:
Gradually add flour mixture to the wet ingredients, alternating with milk. Mix until combined. Stir in vanilla.

Fill muffin tin:
Divide batter evenly between muffin cups, filling each about ⅔ full.

Bake:
Bake for 20–25 minutes, until muffin edges are golden and a toothpick inserted in the center comes out clean.

Coat in cinnamon sugar:
While muffins are still warm, dip each top into melted butter for about 10 seconds, then roll in the cinnamon sugar mixture. Coat generously.