Preheat the oven to 375°F. Spray or oil muffin tins.
In one bowl, mix the bananas with the buttermilk, sugar, egg, and oil, then add the oats. In another bowl, combine the flour, nutmeg, and baking soda. Pour the wet ingredients into the dry and quickly stir them together.
Fill the muffin tins two-thirds full. (Put a little water in the empty cups.) Bake until golden brown and springy when pressed lightly with a finger, about 25 minutes. Run a knife around the edge of each muffin and remove.