Preheat oven to 350°F (175°C). Grease a 9x5-inch loaf pan with butter or nonstick spray and line the bottom with parchment paper, letting the excess hang over the long sides.
In a large bowl, beat melted butter, granulated sugar, and brown sugar until combined. Add eggs one at a time, beating well after each. Stir in vanilla and mashed banana until smooth.
In a separate bowl, whisk together flour, baking soda, baking powder, salt, and cinnamon until evenly distributed.
Add dry ingredients to wet in two additions, stirring with a spatula only until streaks of flour disappear. Stop mixing as soon as batter looks uniform.
Toss diced peach with reserved flour if not already done. Gently fold peach and walnuts or pecans (if using) into batter just until distributed.
Pour batter into prepared pan and smooth the top. Optionally arrange extra peach slices on top and sprinkle with a pinch of brown sugar for a crackled crust.
Bake on center rack for 55 to 65 minutes. Check at 45 minutes and tent with foil if top is browning too quickly. Bread is done when toothpick inserted in center comes out clean or with moist crumbs.
Cool in pan for 15 minutes, then use parchment to lift onto a wire rack. Cool for at least 45 minutes before slicing.