Heat the oven to 375°F. Grease a 9 by 5-inch loaf pan with some of the oil. Mash the bananas in a large bowl. Add the rice, maple syrup, vanilla, and the remaining oil; stir until thoroughly combined.
Put the flour, baking powder, salt, and spices in a medium bowl; stir until everything is evenly distributed.
Fold the dry ingredients into the rice mixture along with the nuts. Gently stir until the mixture is just combined.
Pour the batter into the prepared pan and bake for 45 to 50 minutes, or until a toothpick poked into the middle comes out clean. Let sit on a wire rack for 10 to 15 minutes before inverting, then cool completely before slicing. (Store loosely wrapped in the refrigerator for up to a day or two, or freeze in an airtight container for up to a couple months.)