1. Preheat the oven to 350°F. Lightly butter an 8½ × 4½-inch loaf pan and set aside.
2. Sift together the flour, baking powder, and baking soda and set aside.
3. Put the butter, honey, sugar, cinnamon, and salt in the bowl of an electric mixer fitted with the paddle attachment. Beat the mixture on medium-high speed until light and fluffy, about 5 minutes. Scrape down the sides and bottom of the bowl, add the bananas and vanilla, and beat on medium speed until the mixture looks “broken,” or lumpy, about 1 minute. The bananas should be smashed, with a few small chunks remaining.
4. Turn the speed to medium-low and beat in the egg until incorporated. Turn the speed to low and gradually add the sifted flour mixture, mixing just until no traces of flour remain, about 10 seconds. Add the yogurt and mix until the batter has only a few remaining white streaks, about 5 seconds. Be sure to avoid overmixing. Gently fold in the chocolate chips, if desired.
5. Transfer the batter to the greased pan. Bake in the center of the oven until a tester inserted in the center comes out clean, about 45 minutes. Cool the cake in the pan on a rack for 5 minutes, then unmold and cool completely on the rack.