Preheat the oven to 350° F. Grease 8-inch or 9-inch loaf pan with nonstick spray or butter. Set aside.
Sift flour, baking soda, baking powder, salt, and ground cinnamon together and whisk well. Set aside.
In a large mixing bowl, take mashed bananas. You can mash bananas either with a fork or blend them into a blender. You can also use a stand mixer with a paddle attachment to mash bananas.
Add melted butter and brown sugar. Mix until everything is well combined.
Now add sour cream and vanilla, mix well until combined and the mixture is smooth.
Add dry ingredients and mix until just combined. Do not overmix.
Fold in chocolate chips into the batter and mix gently to distribute evenly.
Pour the batter into a prepared loaf pan.
Bake the banana bread in a preheated oven for 45-55 minutes or until a wooden skewer inserted into the center comes out clean.
Keep an eye on the bread. If the top of the bread is browning too quickly, after 30 - 35 minutes, remove it from the oven and loosely cover with aluminum foil. Return it to the oven and continue baking for the remaining time.
Remove the bread from the oven and transfer the loaf pan onto a wire rack. Allow the bread to cool completely into the pan.
Once it is cooled, remove it from the pan, slice, and serve. You can keep the eggless banana bread tightly covered at room temperature for up to 4 days.