1Preheat oven to 325 degrees F (165 degrees C). Line 12 muffin cups with papers liners.
2Beat sugar and butter with an electric mixer in a large bowl until smooth and creamy. Beat first egg into the butter until completely blended; beat in the vanilla extract with the remaining egg.
3Mix bananas, milk, and allspice together in a separate bowl; stir into the creamed butter mixture. Whisk flour, baking powder, and baking soda together in a separate bowl; slowly stir into banana-butter mixture until batter is just mixed. Fold oats and walnuts into batter. Scoop batter into the muffin cups using a large ice cream scoop.
4Bake in the preheated oven until a toothpick inserted in the center comes out clean, 25 to 35 minutes.