Preheat the oven to 350°F (175°C). Grease a 9×5-inch loaf pan with nonstick cooking spray or butter and set aside.

In a medium bowl, whisk together 1 3/4 cups all-purpose flour, 1 teaspoon baking powder, 1/4 teaspoon salt, and 1/8 teaspoon baking soda; set the dry mixture aside.

In the bowl of a stand mixer or a large mixing bowl using a hand mixer, cream 1/2 cup softened unsalted butter and 1 cup granulated sugar on medium speed until light and fluffy, about 2–3 minutes.

Add the 2 large eggs one at a time, mixing briefly after each addition until incorporated.

Add 1 cup mashed brown bananas, 1/4 cup buttermilk, and 1/2 teaspoon vanilla extract. Mix on low speed (or stir by hand) until the wet ingredients are combined.

Add the reserved dry ingredients to the wet ingredients. Fold or mix on low speed just until no streaks of flour remain; do not overmix.

Pour the batter into the prepared 9×5-inch loaf pan and smooth the top with a spatula.

Bake in the preheated oven for 50–55 minutes, or until a toothpick inserted into the center comes out clean or with a few moist crumbs.

Transfer the pan to a wire cooling rack and let the bread cool in the pan for 15 minutes. Run a knife around the edges, remove the loaf from the pan, and let it cool completely on the rack before slicing and serving.