Preheat the oven and get the pan ready. Preheat the oven to 350°F and adjust a rack to the center. Add 1 tablespoon of the melted butter to a 10-inch bundt pan and move it around and so it's completely coated. (Using a pastry brush or your hands will help.) Then sprinkle 1 tablespoon of the cocoa powder as evenly as possible over the butter. Set aside.
Mix dry ingredients. In a medium-sized mixing bowl, combine the remaining ⅔ cup cocoa powder, gluten-free flour, baking powder, and baking soda. Stir until everything is evenly incorporated and set aside.
Mix the wet ingredients. In a large mixing bowl, use an electric mixer to beat the eggs, sugar, vanilla and salt together. Mix on high until it's a thick and pale yellow, about 2 minutes. Once it's blended add the sour cream and mix until it's smooth.
Combine the dry ingredients with the wet, and add butter. Gradually fold the dry ingredients into the wet, mixing just until everything is well incorporated. Now fold in the remaining 1 cup melted butter.
Remove excess liquid from the zucchini. Use your hands to "wring out" the zucchini, to remove some of the liquid -- only what seems to drip off easily. Fold the zucchini into the batter and then immediately pour into the prepared bunt pan.
Bake. Place in the preheated 350°F oven until the cake no longer jiggles when the pan is moved, and it's starting to crack on top, about 35 to 45 minutes.
Cool. Let it cool in the pan for about 10 minutes, then invert it on a large platter. Let it cool for about an hour before serving.