Heat the oven to 350°F (175°C). Grease the loaf pan and line the long sides with a parchment sling, leaving handles for lifting.
Mash ripe bananas until mostly smooth with a few small lumps. Measure the mash rather than relying on the number of bananas, which vary in size.
Whisk flour, baking soda, salt, and cinnamon in a bowl. In another bowl whisk cooled melted butter and brown sugar until evenly blended.
Whisk eggs, measured banana, sour cream, and vanilla into the butter mixture. Scrape the bowl so the fruit is distributed through the wet base.
Fold dry ingredients into the banana mixture just until no flour streaks remain. Do not beat the thick batter into a completely smooth paste.
Scrape into the pan and level the top. Bake 55–65 minutes until a skewer in the center shows moist crumbs but no raw batter.
Tent with foil if the top darkens before the center cooks. Cool in the pan for 15 minutes, then lift onto a rack to cool about 1 hour.
Slice with a serrated knife once the crumb has set. Cool the remaining loaf completely before wrapping so steam does not make the surface sticky.