Preheat the oven to 425°F (220°C). Line all 12 cups of a standard muffin pan with paper liners. Lightly grease the liners if they are not labeled nonstick.

Place the peeled bananas in a large mixing bowl. Mash them with a fork until mostly smooth. A few small pieces are fine, but large chunks can create wet pockets in the baked muffins.

Add the melted butter and brown sugar to the mashed bananas and whisk until evenly blended. Add the eggs, sour cream, and vanilla, then whisk until the mixture looks smooth and no streaks of egg remain.

In a medium bowl, whisk together the flour, baking soda, cinnamon, baking powder, and salt. Break up any compacted flour so the leavening is evenly distributed.

Add the dry ingredients to the banana mixture: Fold gently with a flexible spatula until only a few small flour streaks remain. Fold in the optional walnuts or pecans, if using, and stop mixing as soon as the batter is uniform. It should be thick and scoopable rather than pourable.

Divide the batter evenly among the 12 prepared cups. Each cup should be nearly full. Smooth any tall peaks lightly so they do not brown too quickly.

Bake the muffins at 425°F (220°C) for 5 minutes. Without opening the oven door, reduce the temperature to 350°F (175°C).

Continue baking for 15 to 18 minutes. The muffins are done when the tops are golden, the centers spring back lightly, and a toothpick inserted into the middle comes out clean or with a few moist crumbs. Wet batter means they need another 2 to 3 minutes.

If the tops become dark before the centers are done, place a loose sheet of aluminum foil over the pan and continue baking. Do not seal the foil around the edges.

Place the muffin pan on a wire rack and let the muffins cool for 5 minutes. They will be soft and delicate immediately after baking.

Transfer the muffins from the pan to the wire rack. Cool for at least 10 more minutes before serving so the crumb can finish setting.