Combine 2 cups of the flour and the yeast in a large mixing bowl; set aside.
Heat and stir milk, the 1/3 cup sugar, the 1/3 cup butter or margarine, and salt in a medium saucepan until warm (120 degrees F to 130 degrees F) and butter or margarine almost melts. Add to flour mixture. Add eggs and 1/2 cup orange juice. Beat with an electric mixer on low to medium speed for 30 seconds, scraping the sides of the bowl. Beat on high speed for 3 minutes. Using a wooden spoon, stir in dried cherries or cranberries and as much of the remaining flour as you can.
Turn dough out onto lightly floured surface. Knead in enough of the remaining flour to make a moderately stiff dough that is smooth and elastic (6 to 8 minutes total). Shape dough into a ball. Place dough in a lightly greased bowl, turning once to grease entire surface. Cover and let rise in a warm place about 1 hour until doubled.
Punch dough down; turn out onto a lightly floured surface. Divide dough in half. Cover and let rest for 10 minutes. If baking immediately, grease two foil lined baking sheets; set aside.
For filling, combine the 2/3 cup sugar, the 1/4 cup butter or margarine, the 1 tablespoon flour, and 1 teaspoon orange peel. Roll each half of dough into a 14x10-inch rectangle. Spread filling lengthwise over half of each rectangle. Fold dough in half lengthwise, covering the filling. Cut each rectangle into fourteen 1-inch-wide strips. Holding a strip at both ends, carefully twist one end in one direction and the other end in the opposite direction. Repeat with other strips.
Place strips on prepared baking sheet, pressing ends down. Cover and let rise in a warm place about 30 minutes until nearly doubled. Bake in a 375 degree F oven for 15 to 18 minutes or until lightly browned.
Remove twists from baking sheets and place on a wire rack.
Stir together sifted powdered sugar, 1 teaspoon orange peel, and enough orange juice (2 to 3 tablespoons) to make the icing easy to drizzle. Drizzle over rolls. Makes 28.
Cover unbaked twists with oiled waxed paper, then with plastic wrap; chill for 2 to 24 hours. Uncover twists and let stand at room temperature 30 minutes. Break any surface bubbles with a greased wooden toothpick. Prepare baking sheets and bake as directed above.
Or, place baked and cooled unfrosted twists in a freezer container or bag, and freeze up to 1 month. To reheat, place twists on two baking sheets. Bake in a 350 degree F oven about 10 minutes or until heated through. Drizzle with Orange Icing.