Preheat oven to 425 degrees. Grease an 8-inch round cake pan and line bottom with parchment. Grease again.
In a medium bowl, whisk together flour, baking powder and salt.
With a handheld mixer or by hand, beat softened butter, oil, half the sugar, brown sugar, molasses, allspice, cinnamon, espresso (if using) and vanilla until just combined. Add the remaining sugar. The undissolved sugar supposedly improves the texture.
Stir the egg into butter mixture, then stir in flour mixture until fully blended.
Fold in bananas and chocolate chips last.
Scrape batter into prepared cake pan and bake until top is golden and sides begin to pull away from pan, about 25 minutes. I baked for the full 25 minutes. Edges were on the overly browned side, but they tasted great.
Let cool completely then run a thin spatula around the edges to separate from the pan. Invert onto a serving plate.