For the doughnut muffins: Preheat the oven to 350 degrees F. Lightly grease two 24-cup mini muffin tins with butter.
In a large bowl, stir together the flour, baking powder, salt and nutmeg. Set aside. In a different bowl, cream together the sugar and butter. Add the eggs and mix again. Add the flour mixture and milk alternately to the creamed mixture, beating well after each addition.
Fill the prepared mini muffin pans two-thirds full. Bake until golden, 10 to 15 minutes.
For the cinnamon sugar topping: Mix the sugar, cinnamon and cocoa in a shallow bowl.
Roll the muffins in the melted butter, coating them completely, then roll them in the cinnamon sugar. Transfer to a cooling rack.