Preheat the oven to 350 degrees . Grease a 9-inch square metal baking pan and line the bottom with parchment; grease the parchment.
In a large bowl, combine the flour, cocoa, baking powder, espresso powder and salt. Using an electric mixer, beat the sugar, eggs and egg whites at medium-high speed until pale in color, about 3 minutes; whisk in the olive oil. Stir in the zucchini. Stir in the flour mixture and 1 container yogurt alternately in 2 batches. Transfer to the prepared pan.
Bake until springy to the touch and a cake tester comes out with moist crumbs, about 35 minutes; let cool slightly. Serve warm with the remaining yogurt.
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