Preheat oven to 350°F (175°C) with rack in center position. Grease a 9x5-inch loaf pan with butter or non-stick spray, dust with flour, and tap out excess (or line with parchment paper).
Peel the overripe bananas into a large mixing bowl and mash with a fork or potato masher until mostly smooth with a few small lumps. Measure out 1½ cups (340g).
Stir melted butter into mashed bananas, then mix in sugar, beaten egg, and vanilla extract until smooth. Fold in sour cream until fully incorporated with no streaks.
In a separate medium bowl, whisk together flour, baking soda, salt, and cinnamon until evenly distributed with no clumps of baking soda.
Add dry ingredients to wet ingredients all at once and fold with a rubber spatula using broad sweeping motions just until no dry flour remains — do not overmix. The batter will be thick and slightly lumpy.
In a small bowl, stir together 3 tablespoons sugar and 1½ teaspoons cinnamon, then mix in 1 tablespoon melted butter until the mixture is crumbly and sandy.
Pour batter into prepared loaf pan and spread evenly; tap pan on counter a few times to release air bubbles. Sprinkle cinnamon-sugar topping evenly over the entire surface, including edges.
Bake for 60–65 minutes until a toothpick inserted in the center comes out clean or with just a few moist crumbs. If the top browns too quickly after 45 minutes, tent loosely with aluminum foil.
Place the pan on a cooling rack and let cool for 15 minutes, then run a knife around the edges and turn out the loaf. Cool at least 30 minutes before slicing for clean cuts.