In a large bowl, sift together the flour, sugar, baking powder, cinnamon, nutmeg, and salt.
In a small bowl, whisk together the egg, milk, melted butter, and vanilla. Stir the wet mixture into the dry ingredients until just combined.
Spoon the batter into the baking pans, filling each one a little more than three-quarters full. Bake for 17 minutes, until a toothpick comes out clean.