Heat the oven to 350°F (175°C). Grease a 9 × 5-inch loaf pan and line it with parchment paper, leaving an overhang on the long sides.
In a large bowl, mash the bananas with a fork until mostly smooth.
Add the melted butter, brown sugar, egg, and vanilla. Stir until well combined.
Sprinkle the baking soda, salt, and cinnamon over the batter and stir briefly. Add the flour and fold until just combined, with no dry streaks remaining.
Gently fold in ¾ cup of the chocolate chips.
Pour the batter into the prepared pan, smooth the top, and scatter the remaining 2 tablespoons of chocolate chips over the surface.
Bake for 55 to 65 minutes, until a toothpick inserted into the center comes out with a few moist crumbs. Cover loosely with foil after 40 minutes if the top browns too quickly.
Cool in the pan for 15 minutes, then lift out and cool on a wire rack for at least 30 minutes before slicing.