Preheat oven to 180°C, butter and flour a square baking pan about 20x20 cm (8x8 in.).
Melt the dark chocolate with the butter in a double boiler; stir until smooth. In a bowl, beat the eggs with the sugar and vanilla extract until frothy. Add the melted chocolate to the egg mixture and mix gently. In another bowl, sift the flour with the unsweetened cocoa and salt. Gradually incorporate the dry ingredients into the wet mixture, stirring gently until smooth. Add the grated and squeezed zucchini to the mixture and mix well.
Pour the mixture into the prepared baking dish and level the surface. Bake for about 25-30 minutes or until the center is still slightly moist. Do the toothpick test: if it comes out with a few moist crumbs, it is ready.