Preheat the oven to 350 degrees F. Spray a 9- by 5-inch loaf pan with cooking spray.
Pulse the avocado, egg, vanilla and zest in a food processor until smooth. Transfer the mixture to a large bowl, and fold in the bananas.
Whisk together the flour, cocoa powder, sugar, baking soda, cinnamon, salt and allspice in a medium bowl. Fold the flour mixture and 1/2 cup of the chocolate chips into the avocado mixture until just combined (it's OK if there are some lumps). Transfer the batter to the prepared loaf pan, and sprinkle with the remaining 2 tablespoons chocolate chips. Bake until a toothpick inserted in the center comes out clean, 1 hour to 1 hour 10 minutes. Run a knife around the edges, and let cool completely in the pan on a rack. The bread can be stored at room temperature in an airtight container for up to 3 days.
When measuring flour, we spoon it into a dry measuring cup and level off the excess. (Scooping directly from the bag compacts the flour, resulting in dry baked goods.)
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