Position a rack in the center of the oven and preheat to 350ºF. Line a 9x12-inch baking pan with parchment paper on all sides.
Place the butter and vanilla pod and scrapings in a medium, heavy saucepan. Melt the butter over medium-low heat, then continue cooking the butter until it turns golden and smells nutty, swirling the pan to prevent burning, 3-5 more minutes. Pour the butter into a large, heat-proof bowl and let cool to warm. Whisk in the brown sugar, banana, egg yolks, and buttermilk. Place a strainer over the bowl and add the sweet rice, coconut, millet, and tapioca flours along with the baking powder, baking soda, and salt. Sift into the wet ingredients, and stir to combine.
In the bowl of a stand mixer fitted with the whip attachment (or in a large bowl with an electric beater or whisk) beat the egg whites on medium-high until foamy. Gradually add the sugar and continue beating until the whites hold soft peaks. Gently fold one-third of the whipped whites into the batter, then fold in the remaining egg whites.
Scrape the batter into the prepared pan and smooth the top. Bake the cake until golden on top and a toothpick inserted near the center comes out clean or with a few moist crumbs, 40-50 minutes. Remove from the oven and let cool completely in the pan.
Make the frosting:
Prepare the butterscotch sauce, cool, and chill until needed.
Make the cream cheese frosting and reserve at room temperature until needed.
Finish the cake:
Spread the frosting over the cooled cake. Dollop and drizzle some of the butterscotch sauce over the frosting, and use the back of a spoon to swirl it into the frosting. Serve slices of cake with extra butterscotch sauce if you like.
The cake is best served at room temperature, but extras can be chilled airtight for up to 4 days.
Nutritional values are based on one of twelve servings.