Preheat oven to 350°F and prepare pan: grease a 9x5 inch loaf pan with butter or nonstick spray, then line bottom with a parchment paper strip for easy removal.
In a large bowl, mash bananas with a fork until mostly smooth, leaving a few small lumps. Whisk in eggs, melted butter, brown sugar, granulated sugar, vanilla, and sour cream until smooth and combined, about 1 minute.
In a separate medium bowl, whisk together 1 3/4 cups flour, baking soda, baking powder, salt, cinnamon, and nutmeg until evenly combined.
Pour dry mixture into wet mixture and fold with a rubber spatula just until no streaks of flour remain, being careful not to overmix.
In a small bowl, toss diced peaches with the remaining 1 tablespoon flour to lightly coat. Gently fold coated peaches and pecans into batter using just a few strokes.
Pour batter into prepared loaf pan and spread evenly. Mix turbinado sugar with a pinch of cinnamon and sprinkle over the top.
Bake for 55-65 minutes. Check at 40 minutes; tent loosely with foil if top is browning too quickly. Bread is done when a toothpick inserted in center comes out clean or with moist crumbs.
Cool in pan on a wire rack for 15 minutes, then lift out using parchment paper and transfer directly to the rack. Cool for at least 30 more minutes before slicing.