Preheat your oven to 350°F (175°C). Grease a 9x5-inch metal loaf pan with butter or non-stick spray, then line it with parchment paper, leaving an overhang on the long sides for easy removal. Using a metal pan rather than glass ensures heat conducts evenly, preventing the edges from over-baking before the center is set.
In a medium mixing bowl, vigorously whisk together the gluten-free flour, baking soda, baking powder, kosher salt, cinnamon, and nutmeg. Whisking aerates the dense gluten-free flour, breaking up any microscopic lumps and ensuring the leavening agents are perfectly distributed throughout the batter.
In a large mixing bowl, thoroughly mash the overripe bananas with a fork until they reach a relatively smooth, pudding-like consistency with only small lumps remaining. The finer the mash, the more evenly the moisture and natural sugars will permeate the crumb.
To the mashed bananas, add the melted butter and brown sugar, whisking vigorously until homogenous. Add the room temperature eggs one at a time, whisking well after each addition, followed by the vanilla extract and Greek yogurt. Room temperature eggs emulsify seamlessly into the batter, whereas cold eggs will cause the melted butter to seize and create an uneven, greasy texture.
Gently fold the dry ingredient mixture into the wet ingredients using a rubber spatula. Mix only until no visible streaks of dry flour remain. Even though there is no gluten to overwork, over-mixing can still result in a dense loaf by knocking out the air bubbles created by the eggs and baking soda.
Let the batter sit undisturbed in the bowl for exactly 15 minutes. This is a crucial technique in gluten-free baking; it allows the rice flours and starches time to fully hydrate and soften, which eliminates the gritty texture often found in inferior recipes.
Pour the rested batter into the prepared loaf pan, smoothing the top with your spatula. Bake on the center rack for 55 to 65 minutes. Check at the 45-minute mark; if the top is browning too quickly, tent it loosely with aluminum foil. The bread is done when a wooden skewer inserted into the very center comes out clean or with a few moist crumbs attached.
Allow the bread to cool in the pan for 15 minutes before using the parchment overhang to lift it onto a wire cooling rack. You must let it cool completely (at least 2 hours) before slicing. Gluten-free baked goods finish setting up as they cool; slicing while hot will result in a gummy, collapsed interior.
