Prepare Coffee Cake: In cup, combine 1/2 cup warm water (105 to 115 degrees F) with yeast and 1 teaspoon granulated sugar; stir to dissolve. Let stand until foamy, about 5 minutes.
Meanwhile, in large bowl, with mixer at low speed, beat butter and remaining 1/2 cup granulated sugar until blended. Increase speed to high; beat until light and fluffy, about 2 minutes, occasionally scraping bowl with rubber spatula. Reduce speed to low; beat in egg until blended. Beat in yeast mixture, salt, and 1/2 cup flour (batter will look curdled) just until blended. With wooden spoon, stir in 2 1/2 cups flour until blended.
Turn dough onto lightly floured surface and knead until smooth and elastic, about 8 minutes, working in enough of remaining 1/4 cup flour just to keep dough from sticking.
Shape dough into ball; place in greased large bowl, turning dough over to grease top. Cover bowl with plastic wrap and let rise in warm place (80 to 85 degrees F) until doubled in volume, about 1 hour.
Meanwhile, prepare Chocolate-Walnut Filling: In 1-quart saucepan, combine chocolates and condensed milk; heat over low heat until melted and smooth, stirring occasionally. Cool filling to room temperature. Stir in walnuts. Cover and refrigerate until ready to use.
Punch down dough. Turn dough onto lightly floured surface; cover and let rest 15 minutes. Meanwhile, grease large cookie sheet.
With floured rolling pin, roll dough into 18" by 12" rectangle. Spread filling over dough to within 1/2 inch of edges.
Starting at a long side, roll up dough jelly-roll fashion. Carefully lift roll and place, seam side down, on prepared cookie sheet. Shape roll into ring; press ends together to seal. With knife or kitchen shears, cut ring at 1 1/2-inch intervals, up to, but not completely through, inside dough edge. Gently pull and twist each cut piece to show filling. Dough will be soft, so use small metal spatula to help lift pieces. Cover and let rise in warm place until slightly risen, about 1 hour.
Meanwhile, preheat oven to 350 degrees F. Bake coffee cake 30 to 35 minutes or until golden. Transfer coffee cake to wire rack to cool.
Prepare Icing: In small bowl, with spoon, mix confectioners' sugar with milk until smooth. When coffee cake is cool, drizzle with icing.
