Preheat the oven to 350ºF and grease a 9x5-inch loaf pan then line it with a strip of parchment paper.
In a large bowl, combine all of the ingredients and stir until a smooth batter forms. Pour the batter into the prepared pan, smooth the top, then rest the batter until the oven is fully heated.
Bake the loaf for about 50-55 minutes, when a tester comes out clean or with a few moist crumbs.
Cool the bread in the pan for 20 minutes, then cool it on a rack. I like to cool the bread completely so that the crumb sets, but it's OK to cut into it after about 30 minutes (it's delicious warm!).
Notes
Can I use frozen bananas? Absolutely. A great way to save ripe bananas is to freeze them (skin on or off, you decide) in a freezer-safe bag. When you're ready to bake, take out as many bananas as you need, let them defrost in a bowl, and drain away any liquid before mashing them up for the recipe.
Rest the batter. Don't turn the oven on until you have assembled the batter. While the oven is preheating, the oat flour will have time to hydrate (soak up the moisture in the batter), making for a softer, better crumb after the loaf is baked.
Can I use another flour? You can use a gluten-free flour blend instead of the oat flour by weight. Or try another single origin gluten-free flour like sorghum flour or brown rice flour by weight.
Try other spices. Instead of ginger, use ground cinnamon or cardamom. Add a pinch of nutmeg for a slightly different flavor note. Or, add fresh peeled and grated ginger!
Make it refined sugar-free. Substitute coconut sugar or maple syrup for the brown sugar.
Dairy-free: Swap melted dairy-free butter or melted coconut oil for the unsalted butter.