In a small saucepan, bring the prunes and 2 cups of water to a boil over high heat. Reduce the heat and simmer, uncovered, until the prunes are very soft, about 20 minutes. Drain.
Meanwhile, preheat the oven to 350°F. Lightly butter a 5x9-inch loaf pan and line the bottom with a piece of parchment paper, cut to fit.
In a food processor, whirl the prunes and bananas until very smooth. Add the eggs and whirl to combine.
In a large bowl, sift together the flour, cocoa, baking powder, cinnamon, and baking soda. Stir in the banana mixture until evenly moistened. Stir in the banana chips and chocolate chips. Scrape the thick batter into the pan and spread evenly.
Bake the bread until a toothpick inserted into the center comes out a little chocolatey but not gooey, 40 to 50 minutes. Loosen the bread from the pan with a knife and invert onto a rack. Remove the parchment paper. Turn the bread right-side-up and let cool at least 1 hour before slicing.
Notes
Shortcut: Sub 10 ounces (1¼ cups) unsweetened prune baby food for the pitted prunes, and omit water and cooking in step 1.