1) Preheat oven to 350 degrees F. Lightly butter and dust with flour a 9×5 loaf pan.
2) In a large bowl, mash very ripe bananas with sugar. Then whisk in melted butter, sugars, and eggs.
3) In a small bowl, stir together flour, baking soda, and salt. Stir dry ingredients into wet ingredients.
4) Stir in pomegranate arils and chopped pistachios. Transfer to loaf pan.
5) Bake loaf at 350 degrees for 45-50 minutes until a tester comes out clean from the center.
6) Let loaf cool for a few minutes, then remove from pan. Serve warm or let cool completely and wrap tightly to keep fresh.