Grease a 14-inch pizza pan; set aside. On a lightly floured surface, flatten thawed dough slightly. Cut each loaf of dough into 4 pieces (8 pieces total). Form each piece into a rope about 18 inches long. Brush entire surface of each rope with melted margarine or butter.
Stir together the granulated sugar, brown sugar, and cinnamon. Place mixture in shallow pan or on large sheet of foil.
Roll 1 rope in sugar mixture to coat evenly. Shape rope into coil in center of the prepared pan. Roll another rope in sugar mixture. Attach securely to end of first rope and coil around first coil. Continue coating remaining ropes with sugar mixture and attaching them to form a 10- to 11-inch circle. Sprinkle any remaining sugar mixture over ring. Sprinkle chopped pecans on top.
Cover and let rise in a warm place until nearly double (30 to 40 minutes). (Or, cover with plastic wrap and let rise overnight in the refrigerator. Before baking, remove from the refrigerator and let stand 15 to 20 minutes.)
Bake in a 350 degree F oven for 25 to 30 minutes or until bread sounds hollow when lightly tapped. If necessary, cover with foil the last 10 minutes of baking to prevent overbrowning. Cool about 15 minutes.
Stir together powdered sugar, vanilla, and enough milk (about 2 teaspoons) to make a thick glaze. Spoon over ring. Serve warm cut into wedges. Makes 12 servings.