Make the cake. Grease bottom and sides of an 8" round pan and set aside.
In a bowl, combine coconut, condensed milk, and egg white. Mix thoroughly. Transfer coconut mixture to a sheet of plastic wrap. Roll the coconut and form into a rope measuring about 18". Wrap and refrigerate until firm, about 30 minutes. Preheat oven to 350 degrees F.
In another bowl, sift together flour, cocoa powder, baking powder, baking soda, and salt. Set aside.
In separate bowl, beat butter and sugar until fluffy. Add eggs, one at a time, beating well after each addition. Add melted chocolate and vanilla extract. Beat batter until smooth.
Add flour mixture to batter alternately with the yogurt. Pour batter into prepared pan. Unwrap the coconut and form into a circle. Arrange the coconut rope on the center of cake batter.
Bake in preheated oven about one hour or until cake tester inserted in the center comes clean. Let cool.
Make the glaze. In a saucepan, combine sugar and water and bring to a boil. Stir until sugar dissolves. Add cocoa powder and vanilla extract and stir until smooth. Remove from heat and let cool.
Bursh the cooled cake with the glaze. Refrigerate until the glaze is set before serving.