Two types of chocolate -- semisweet and cocoa powder -- give this loaf its rich flavor.
Preheat oven to 350 degrees. Butter a 10-by-5-inch loaf pan. Line with parchment, leaving an overhang on two long sides, then butter and flour paper.
Whisk together flour, sugar, cocoa, baking powder, salt, and baking soda. In another bowl, stir together butter, eggs, vanilla, and zucchini. Stir into dry mixture, then fold in chocolate. Pour into pan, smoothing top with a spatula. Bake until a skewer inserted into the center comes out clean, about 1 hour 20 minutes. Let cool 20 minutes on a wire rack, then remove from pan and cool completely.
In a small bowl, combine sugar and milk. Whisk until smooth. Pour glaze over bread, then sprinkle with poppy seeds. Let stand until set, about 20 minutes, then cut into slices to serve. Bread will keep, unglazed, at room temperature for up to 3 days.