In a large bowl combine warm water and yeast; set aside for 5 minutes
Meanwhile, in a small saucepan, combine milk, 1/4 cup butter, 3 tablespoons granulated sugar, and salt. Heat just until warm (120 degrees F to 130 degrees F) and butter almost melts. Add to yeast mixture along with eggs.
Beat in as much of the 3-1/4 to 3-1/2 cups flour as you can with a wooden spoon. Turn dough out onto a lightly floured surface. Knead in enough of the remaining flour to make a soft dough that is smooth and elastic. Shape dough into a ball. Place in a lightly greased bowl, turning once to grease surface of dough. Cover; let rise in a warm place until double in size, 1 to 1-1/2 hours.
For filling, in a small bowl, stir together the brown sugar, 1/3 cup granulated sugar, 1/4 cup softened butter, maple syrup, 2 tablespoons flour, cinnamon, and maple flavoring, if you like. Stir in walnuts. Lightly grease two 8-inch round baking pans; set aside.
Punch dough down. Divide in half. Cover; let rest 10 minutes. On a lightly floured surface, roll one portion of dough to a 14x8-inch rectangle. Spread on half of the filling. Starting from a long end, roll up the dough and pinch edges to seal. Wrap the ends around to form a ring. Place the ring, seam side down, in one of the prepared pans. Using a small sharp knife, make 8 cuts around the edge of the dough at even intervals, cutting nearly all the way through to the center. Turn each cut portion so the cut side faces up. Repeat with the remaining dough and filling. Cover and let rise 45 minutes or until nearly double.
Bake in a 350 degree F oven for 25 to 30 minutes or until golden brown.
Meanwhile, in a small bowl stir together powdered sugar and enough water to make a drizzling consistency. Drizzle mixture over twists. Serve warm or cooled. Makes 16 rolls.