Preheat oven to 350 degrees F (175 degrees C). Spray a mini muffin tin with cooking spray or line with paper cups.
Place flour, sugar, milk, vegetable oil, egg, baking powder, salt, 1/2 teaspoon nutmeg, and 1/2 teaspoon ground cinnamon in a bowl. Mix dough by hand until well combined but some lumps remain. Fill muffin tin with dough.
Bake in the preheated oven until tops spring back when lightly pressed, but color is not yet golden brown, about 15 minutes.
Pour melted butter into a bowl. Mix 1/3 cup sugar, 1 tablespoon cinnamon, and 1 teaspoon nutmeg together in a separate bowl. Dip muffins in the butter coating; immediately roll in the cinnamon dusting.