Preheat oven to 350°F. Coat a 9-by-5 inch loaf pan with cooking spray and line with parchment paper, leaving a 1-inch overhang on the long sides of the pan.
Whisk eggs, brown sugar, yogurt, oil, vanilla and salt together in a large bowl until smooth. Sift in all-purpose flour, pastry flour, cocoa, baking soda and baking powder. Gently stir to combine until just a few dry streaks remain; fold in zucchini until just combined. Pour the batter into the prepared pan and smooth the top with a spatula. Sprinkle chocolate chips evenly over the surface of the batter.
Bake until a wooden pick inserted in the center comes out clean, 55 to 60 minutes. Let cool in the pan for 15 minutes. Lift out of the pan using the parchment overhang; remove parchment and cool completely on a wire rack, about 1 hour, before serving.
