Preheat your oven to 350°F (175°C). Grease and flour a standard 9x5 inch loaf pan, or line it with parchment paper for easy removal.
In a large mixing bowl, combine the mashed ripe bananas, melted butter, granulated sugar, and light brown sugar. Whisk until well combined.
Beat in the large egg and vanilla extract until the mixture is smooth and creamy.
In a separate medium bowl, whisk together the all-purpose flour, unsweetened cocoa powder, baking soda, salt, and ground cinnamon. This ensures even distribution of the dry ingredients and prevents clumps.
Gradually add the dry ingredients to the wet ingredients, mixing on low speed (or with a spatula) until just combined. Be careful not to overmix; a few streaks of flour are okay.
Gently fold in the semi-sweet, milk, and white chocolate chips. Reserve about 1/4 cup of the chocolate chips to sprinkle on top before baking.
Pour the batter evenly into the prepared loaf pan. Sprinkle the reserved chocolate chips over the top of the batter.
Bake for 50-65 minutes, or until a wooden skewer or toothpick inserted into the center of the loaf comes out clean (or with a few melted chocolate streaks, which is fine!). If the top starts to brown too quickly, you can loosely tent it with aluminum foil.
Let the banana bread cool in the pan for about 10-15 minutes before carefully inverting it onto a wire rack to cool completely. This allows the bread to set and makes it easier to slice.