Preheat your oven to 350°F (175°C). Grease a 12-cup muffin tin thoroughly or line with paper liners.
In a large mixing bowl, whisk together the flour, sugar, baking powder, salt, cinnamon, and nutmeg until evenly combined.
In a smaller bowl, beat the egg lightly with a fork. Add the milk, vanilla extract, and melted butter (cooled). Mix until smooth and combined.
Pour the wet ingredients into the dry ingredients. Gently stir with a spatula or wooden spoon just until no dry flour is visible. Do not overmix - small lumps are okay and desired for fluffy muffins.
Scoop the batter into the prepared muffin cups, filling each about halfway to three-quarters full.
Bake for 20-25 minutes, until a toothpick inserted in the center comes out clean and the tops spring back when lightly touched.
While the muffins bake, prepare the coating. Mix the cinnamon and sugar in one shallow bowl. Melt the butter for dunking in another shallow bowl.
Let the baked muffins cool for about 5 minutes. Dip the top of each warm muffin in melted butter, let excess drip off, then immediately roll in the cinnamon-sugar mixture.
Serve warm and enjoy! These are best eaten fresh but can be stored in an airtight container for up to 2 days.