Preheat oven to 350 degrees. Spray two (6 each) doughnut pans with cooking spray.
In a large mixing bowl, whisk together the flour, baking powder, baking soda, and salt. Add the sugar, eggs, oil, mashed bananas, and 2 teaspoons vanilla. Mix well.
Spoon the batter into the prepared pans, filling the doughnut cavities almost full. Alternatively, you can put the batter into a large food storage bag, cut off about ¼ inch from one of the corners and squeeze the mixture into the pans. Bake for 15 minutes or until the doughnuts spring back when touched lightly and a tooth pick inserted into the center comes out clean. Let cool in the pans for 10 minutes, then move to a wire rack to cool completely.
Put the Sunbutter in a microwave-safe bowl and put in the microwave for 1 minute to soften (or you can heat in a pan over low heat). Add the powdered sugar, vanilla and about 4 tablespoons of rice milk. Stir to combine and add more rice milk, a little at a time, until it is a smooth, spreadable consistency.
Using a small offset spatula or knife, spread some glaze onto each of the cooled doughnuts.