Soak the raisins in 1 tablespoon of water and chill for 2-3 hours. When ready to use, remove them from the refrigerator, squeeze out excess moisture, and pat dry with a paper towel.
Preheat the oven to 380°F (190°C). Line a 12-cup muffin or cupcake pan. Sift the flour, baking powder, baking soda, and salt into a bowl. Add the brown sugar and whisk to combine the dry ingredients. Set aside. In another bowl, combine the quick oats and milk. Set aside.
In a new bowl, beat the egg, then add the vegetable oil and mix. Incorporate the mashed banana and stir well. Make a well in the dry ingredients and pour in the egg, oil, and banana mixture. Fold until fully combined with no traces of flour, then add the oats and milk mixture. Finally, fold in the raisins, being careful not to overmix.
Spoon the batter into each liner until they are 75% to 80% full. Sprinkle some oats on top.
Bake at 380°F (190°C) for 10 minutes. Then reduce the temperature to 350°F (180°C) for another 8-10 minutes, or until a cake tester inserted into the center comes out clean. Transfer the muffins to a wire rack to cool completely before storing them in airtight containers.