Preheat oven to 375 degrees.
Beat together butter and the sugar until well blended, beat in egg.
Sift together flour, baking powder, salt and nutmeg.
Stir dry ingredients alternately with milk into the butter mixture and blend thoroughly.
Spoon about 1 tablespoon of the batter into each well greased mini muffin tin.
Bake for 20 minutes until golden brown.
Prepare coating: melt butter, set aside.
Combine cinnamon and sugar.
Remove muffins from pans.
While still hot, dip each muffin entirely into melted butter, coating evenly.
Roll in cinnamon sugar.
Serve warm or cold.
To freeze: cool thoroughly, wrap in plastic wrap, then put in plastic bags.
To thaw: remove from plastic wrap as needed.