Grease a 9-inch square baking pan well.
Combine flour, cornmeal, sugar, baking powder, cinnamon, nutmeg, and salt.
Whisk together both types of milk, eggs, butter, rum, and vanilla in another bowl.
Combine both mixtures using a wooden spoon, just enough to dampen all ingredients (it will still be a bit lumpy).
Pour into prepared pan and bake until golden brown and cake tester comes out clean, about 45 minutes.
Let cool on rack slightly before cutting into 12 small squares.
“Adapted from the RSVP section of an old issue of Bon Appetit. This recipe was from a resort in the Cayman Islands. This is a sweeter, more cake-like cornbread and has a bit of rum in it.”