Preheat the oven to 325 degrees F. Line two standard-size muffin tins with paper liners.
In a medium bowl, whisk together the flour, baking soda, salt and baking powder in a medium bowl to blend; set aside.
In a large bowl, whisk together the sugar, oil, eggs and vanilla until completely combined. Gently stir in the banana.
Add the dry ingredients to the banana mixture and, using a rubber spatula, fold the batter together until just blended.
Fill the prepared muffin cups about two-thirds full. Bake the muffins until the tops are golden brown and a tester inserted into the center comes out clean, about 25 minutes. Transfer the muffins to a rack and cool slightly before removing and serving. The muffins can be stored in an airtight container at room temperature for up to 4 days, or frozen in a freezer-safe container for up to 1 month.