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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.
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In a medium-sized mixing bowl, cream together the butter, vegetable oil, and sugars till smooth.
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Add the eggs, beating to combine.
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Stir in the baking powder, baking soda, nutmeg, salt, and vanilla.
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Stir the flour into the butter mixture alternately with the milk, beginning and ending with the flour and making sure everything is thoroughly combined.
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Spoon the batter evenly into the prepared pan, filling the cups nearly full.
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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.
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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).
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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.
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Serve warm, or cool on a rack and wrap airtight. Store for a day or so at room temperature.