Preheat the oven to 425 degrees F. Lightly brush a 12-muffin tin with butter and set aside (or use muffin liners).
Stir the flour, baking soda, brown sugar, and cinnamon together in a large bowl; set aside.
Mash the bananas on a plate with a fork. Then whisk the banana, oil, milk, eggs, salt, and vanilla in a medium bowl.
Make a small well in the center of the dry ingredients. Pour wet ingredients into the center; then stir gently with a wooden spoon until the dry ingredients are moistened but still lumpy. Do not over-mix the batter or muffins will come out dense and oddly shaped. Gently fold in the nuts. Divide the batter evenly into the muffin tin.
Put the muffins in the oven and immediately reduce oven temperature to 375 degrees F. Bake until golden brown, about 25 minutes, rotating the pan halfway through the cooking. (Insert a toothpick into the center of a muffin to check if it is done. Toothpick should come out clean). Cool muffins in the pan on a rack for a couple minutes. Turn the muffins out of the pan and cool on the rack. Serve warm or at room temperature.