Preheat oven to 350°. In a large bowl, cream butter and sugars until light and fluffy. Add eggs, one at a time, beating well after each addition. Gradually beat in milk and vanilla. In another bowl, whisk flour, baking powder, salt, nutmeg, cinnamon and baking soda. Add to creamed mixture; stir just until moistened.

Fill greased or paper-lined muffin cups. Bake 18-20 minutes or until a toothpick inserted in center comes out clean. Cool 5 minutes before removing from pan to a wire rack.

Meanwhile, for coating, combine coarse sugar and cinnamon. Dip tops of warm muffins in butter, then coat in cinnamon-sugar.