Preheat the oven to 350ºF (180ºC).
Line 12 regular muffin tins with paper liners or butter/spray the pans. For taller muffins, fill only 9 or 10 paper cups with batter and the remaining, unused muffin spaces with water so the pan doesn't tilt in the oven.
Sift together the dry ingredients in a large bowl: 1 cup all-purpose flour, 1 teaspoon baking powder, ½ teaspoon baking soda, ½ teaspoon salt and ½ cup light brown sugar. Stir to combine.
Whisk 1 egg, ⅓ cup vegetable oil, and 1 teaspoon vanilla extract in a medium bowl. Do not beat, but mix well until no streaks of egg whites remain.
Add ⅔ cup mashed bananas and stir.
Add the wet ingredients all at once to the bowl with the dry ingredients.
Mix until you barely have streaks of flour, but do NOT overmix. It will be lumpy and not completely mixed, and that is fine.
Divide evenly among the muffin cups or muffin liners.
Bake for about 25 minutes, until the top is dry and golden brown, and a cake tester or toothpick inserted in the center comes out clean. Don't overbake.
Let cool on a wire rack and eat warm or let cool down completely.
They are best eaten the day they are made, but they can be kept for a day at room temperature, covered or wrapped.
Store leftovers, covered in plastic wrap or in an airtight container, in the refrigerator for a few days or frozen for a month.