1. MAKE THE CAKE: Preheat the oven to 350°. Butter and flour an 8-cup Bundt pan. In a small bowl, mix the chopped coconut with the condensed milk and egg white. Transfer the coconut mixture to a large sheet of plastic wrap. Using your hands, roll the coconut into an 18-inch rope. Wrap and refrigerate until slightly firm, at least 20 minutes.
2. In another small bowl, sift the flour with the cocoa, baking powder, baking soda and salt. In a large bowl, using an electric mixer, beat the butter until creamy. Add the sugar and beat until light and fluffy. Add the eggs, 1 at a time, beating well after each addition. Add the melted chocolate and the vanilla and beat until the batter is smooth. Beat in the dry ingredients in 3 batches, alternating with the yogurt.
3. Scrape the batter into the prepared pan and smooth the surface. Unwrap the coconut rope and join the ends to form a circle. Lay the coconut rope on the cake batter, centering it in the pan. Press the coconut into the batter until it is submerged in 1 inch of batter. Bake the cake for 1 hour, or until a toothpick inserted in the center comes out clean. Let cool in the pan for 10 minutes, then invert onto a rack to cool completely.
4. MAKE THE GLAZE: In a medium saucepan, combine the sugar and water and bring to a boil; stir to dissolve the sugar. Whisk in the cocoa and vanilla and let cool. Brush a thin layer of the glaze over the cake and let dry slightly. Repeat 3 more times, letting the glaze dry slightly before brushing the cake again. Refrigerate until the glaze is set and slightly cracked before serving.