Preheat oven to 350 degrees F. Butter or grease a Bundt cake pan well; set aside.
In a food processor, pulse together 3 cups flour, sugar, baking powder, baking soda, and salt. Add butter and pulse until mixture resembles coarse cornmeal.
Combine orange juice and grated rind with well beaten eggs. Pour into dry ingredients and mix until just combined.
Dust the halved cranberries with remaining 1 tablespoon of flour. Carefully fold halved cranberries into batter. Spoon the batter into prepared Bundt pan.
Bake in preheated oven for 40 to 50 minutes or until a cake tester inserted in center comes out clean.
Cool bread in pan on a wire rack for 10 minutes before removing to cool.
Add confectioner's sugar to a small mixing bowl. Add milk 1 tablespoon at a time until glaze is spreadable, but not runny. Spread generously over warm cake allow glaze to run down the sides of the bread.