FOR THE DOUGH: Sprinkle yeast over the water in large bowl of electric mixer. Add 1 teaspoon of the sugar. Let stand until yeast is soft (about 5 minutes).
Add the remaining sugar, milk, salt, vanilla, and butter.
Add 2 cups of the flour, mix to blend, then beat at medium speed until smooth and elastic (about 5 minutes). Beat in egg yolks, one at a time. Stir in about 1 1/4 cups more flour to make a soft dough. You can use a wooden spoon or hands to mix also.
Turn dough out onto a board or pastry cloth coated with some of the remaining 1/4 to 1/2 cup flour. Knead until dough is smooth and satiny and small bubbles form just under surface about 10 to 12 minutes, adding just enough flour to prevent dough from being sticky.
Turn dough in a greased bowl. Cover with plastic wrap and a towel; let rise in a warm place until doubled in bulk about 1 hour. Punch dough down. Cover with inverted bowl and let rest for 10 minutes.
Roll dough out on a floured surface to make a 16-inch square. Spread with Spiced Walnut Filling, leaving a 1/2-inch margin on all edges. Starting at one side, roll up jelly-roll fashion; pinch to seal edge. Cut roll into 1-inch slices.
Place slices, on edge, in a well-greased, 10-inch angel food cake pan; overlap slices, pulling every other one to outside edge of pan (slices between should be pulled to inside edge of pan). Let rise until almost doubled in bulk (40 to 50 minutes). Preheat oven to 375°F.
Bake until coffee cake is richly browned (35 to 40 minutes). Let stand in pan on a wire rack for 10 minutes. Then remove pan sides and tube; transfer cake to rack. While warm drizzle with Powdered Sugar Icing and sprinkle with 1 Tablespoon ground walnuts (reserved from filling). Let cool to room temperature before slice to serve.
FOR THE SPICED WALNUT FILLING: Preheat oven to 350°F Spread walnuts in a shallow pan. Bake until they are golden brown and smell fragrant (10 to 12 minutes) Let cool slightly, then place all the walnuts in food processor (or half the walnuts at a time in blender); process or whirl until finely chopped. Set aside 1 Tablespoon chopped walnuts for decoration. In a medium bowl combine sugar and cinnamon. Mix in the remaining chopped walnuts, butter, and vanilla. Then blend in egg.
POWDERED SUGAR ICING: In a small bowl combine sugar, butter, and vanilla. Gradually blend in water until icing is smoothly mixed and of a good consistency for drizzling.