Grind 1 star anise, ½ teaspoon cloves, and ½ teaspoon allspice in a clean electric grinder dedicated to spices. Sift the blend through a coarse sieve and grind any larger pieces once more.
Preheat the oven to
340 °F. Grease a 9x13-inch sheet pan with ½ Tablespoon butter and dust it with 2 Tablespoons breadcrumbs , or line it with parchment paper. Peel 2 medium zucchini; if it is overgrown, cut it lengthwise and scoop out the tough seeds. Grate it finely on the small holes of a grater into a bowl and keep all the juice.
In a large bowl, combine 2 ½ cups all-purpose flour, 1 ½ teaspoon baking powder, 2 Tablespoons cocoa powder , 1 teaspoon ground cinnamon, the ground spice blend, and 1 Tablespoon lemon zest.
With an electric mixer on high speed, beat 3 eggs, adding 1 ¼ cups granulated sugar gradually, until the mixture is a pale, airy foam; this takes a good 5 minutes.
With the mixer on low speed, work ½ cup sunflower oil into the egg foam in a few additions, then the dry mixture the same way. Finally, stir in the grated zucchini with its juice. Only if the batter is too thick to spread, add 1-2 Tablespoon milk.
Pour the batter onto the prepared pan, smooth the surface, and bake for about 35 minutes. Insert a wooden toothpick into the middle; when it comes out dry, the cake is done.
Before serving, dust the surface with 2 Tablespoons powdered sugar.