In a large bowl, dissolve yeast in the 1/2 cup warm water. Stir in egg. In a small saucepan, heat and stir the 1/2 cup butter, 1/2 cup water, 1/4 cup sugar and salt until mixture is lukewarm and butter is almost melted. Stir butter mixture into the yeast mixture. Stir in flour.
On a lightly floured surface, knead the dough for 4 to 6 strokes or until ingredients are combined. Transfer to a greased bowl. Cover with greased plastic wrap; chill if you like for 8-24 hours.
Let dough stand, covered, at room temperature for 1 hour. Meanwhile, lightly grease baking sheet. Divide dough in half. On a lightly floured surface, roll each half of dough into a 14X9 inch rectangle. Spread the melted butter over dough rectangles. In a small bowl, mix nuts, 1/2 cup sugar, brown sugar and cinnamon. Cut each rectangle into 3 14X3 inch strips. Sprinkle the mixture in the center of each strip. Using your fingers pinch dough to seal.
To shape a loaf, place 3 filled ropes, seam side down, 1 inch apart. Starting at the middle, loosely braid by bringing the left rope over the center rope. Next bring the right rope over new center rope. Repeat to end. Press ends together to seal; tuck under. Repeat to make a second loaf. Carefully transfer braids to cookie sheet. Cover and let rise for 1 hour.
Preheat oven to 350°F Bake for 20-25 minutes or until loaves sound hollow when lightly tapped. Immediately remove loaves from baking sheet. Cool on wire racks. Meanwhile, in a medium bowl, combine 11/2 cup sifted powdered sugar, 1 tbsp milk, and 1/2 teaspoons vanilla. Stir in additional milk, 1 teaspoons at a time, until icing is easy to drizzle. Drizzle icing on loaves.