Heat the oven to 425°F. Line a 12-cup muffin tin with paper liners or grease it well.
Mash the bananas in a large bowl until mostly smooth. Whisk in the melted butter, brown sugar, eggs, sour cream, and vanilla until combined.
Add the flour, baking soda, salt, and cinnamon directly on top. Stir with a spatula just until the flour disappears — a few lumps are fine. Do not overmix.
Fold in the chocolate chips with just a few strokes.
Divide the batter among the 12 cups, filling each nearly to the top. Scatter a few extra chocolate chips over each.
Bake at 425°F for 5 minutes, then — without opening the oven — reduce the temperature to 350°F and bake 13 to 15 minutes more, until a toothpick comes out with moist crumbs. Cool in the pan 5 minutes, then transfer to a rack.