Preheat the oven to 425°F. Lightly grease a standard muffin tin. Or line with 12 paper or silicone muffin cups, and grease the cups with non-stick vegetable oil spray; this will ensure that they peel off the muffins nicely.
In a medium-sized mixing bowl, cream together the butter, vegetable oil, sugars and vanilla till smooth.
Add the eggs, beating to combine.
Stir in the baking powder, baking soda, nutmeg and salt.
Stir the flour into the butter mixture alternately with the milk, beginning and ending with the flour and making sure everything is thoroughly combined.
Spoon the batter evenly into the prepared pan, filling the cups nearly full.
Bake the muffins for 15 to 17 minutes, or until they're a pale golden brown and a cake tester inserted into the middle of one of the center muffins comes out clean.
Remove them from the oven, and let them cool for a couple of minutes, or until you can handle them. While they're cooling, melt the butter for the topping (this is easily done in the microwave).
Use a pastry brush to paint the top of each muffin with the butter, then sprinkle with the cinnamon-sugar. Or simply dip the tops of muffins into the melted butter, then roll in the cinnamon-sugar.
Serve warm, or cool on a rack and wrap airtight. Store for a day or so at room temperature.