Preheat oven to 400.
Line two standard 6-cavity muffin pans with paper cups and spray each cup with a nonstick spray. You can also use a 12-cavity cupcake pan.
Place the oats and eggnog in a bowl and let stand for 20 minutes.
Sift together the flour, baking powder, baking soda, salt, and cinnamon.
In a separate bowl, lightly beat the eggs.
Stir the eggs into the eggnog mixture; mix in the vanilla, rum, brown sugar, and vegetable oil.
Pour the eggnog mixture into the flour mixture and stir just until combined. Do not overmix.
Divide the batter evenly among the prepared muffin cups, sprinkling turbinado sugar on top of each muffin.
Bake for 15 to 20 minutes.
Let cool for 5 minutes before turning them out onto a cooling rack.