1. Preheat the oven to 350°F. Lightly grease 2 mini muffin pans or 1 regular muffin pan. Set aside.
2. In a large bowl, using a mixer, cream together the butter, canola oil, and sugars till smooth. Add the eggs, beating to combine.
3. In a medium bowl, whisk together the flour, baking powder, baking soda, nutmeg, salt, and vanilla.
4. Add the dry ingredients into the butter mixture alternately with the eggnog, beginning and ending with the flour and making sure everything is thoroughly combined.
5. Spoon the batter evenly into the prepared pans, filling the cups nearly full. Bake the muffins for 10-12 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 muffins from the oven, and let them cool for a couple of minutes.
6. To make the glaze, combine butter, sugar, eggnog, vanilla, cinnamon, and nutmeg in a large bowl. Whisk until smooth. Dip the tops of each muffin into the glaze and let cool on a wire cooling rack until glaze sets up.