Preheat your oven to 350°F and line a 12-cup muffin tin with paper liners. If you're using dark-colored pans, watch them closely as they tend to brown faster.
In a medium bowl, whisk together the flour, baking powder, salt, and nutmeg. The nutmeg gives the muffins their warm, bakery-style flavor, so don’t skip it! Stir well to evenly distribute the baking powder.
In a large bowl, whisk together the sugar and oil until the mixture looks like wet sand. Add the egg and beat until the mixture lightens in color and becomes fluffy – about 30 seconds of whisking. Then pour in the milk and vanilla, whisking until combined.
Add the dry ingredients to the wet mixture in two batches, gently stirring with a rubber spatula until the dry flour disappears. The batter should be slightly lumpy – overmixing will make the muffins tough.
Fill each muffin cup about ⅔ full (about 3 tablespoons per muffin). Tap the pan gently on the counter to remove air bubbles.
Bake for 18-20 minutes, or until the tops spring back when lightly pressed and the edges start to turn golden brown. You’ll also notice a few small cracks on top when they’re done.
While the muffins are baking, mix cinnamon and sugar in a shallow bowl and melt butter in a separate bowl. Once the muffins are cool enough to handle (but still warm), brush each one with melted butter and roll in the cinnamon-sugar mixture. Coat all sides, including the top.