Stir warm water, yeast and sugar together in a small mixing bowl; let stand 10 minutes, until mixture foams.
Whisk together 3 eggs, 1 egg white (reserve yolk), oil, salt, and cinnamon in a large mixing bowl. Stir in yeast mixture and 5 1/4 cups flour until soft dough forms. Add sweetened dried cranberries and with floured hands, knead dough. Gradually add remaining 3/4 cup flour, knead dough until smooth and elastic, about 5 minutes.
Lightly grease a large mixing bowl. Place dough in bowl and roll around so that it is lightly coated with oil. Cover bowl with a clean kitchen towel and place in a warm place until doubled in size, about 2 hours.
Punch down dough; divide in half. Each half will make one braided loaf. To make a single braid; divide half into 3 equal pieces. Roll each into a 14-inch rope. Braid dough and pinch ends to seal. Place on a greased baking sheet. Repeat steps with remaining dough.
Cover shaped loaves and let rise in a warm place until doubled in size, about 1 hour. Preheat oven to 400 degrees F. Beat reserved egg yolk with 1 teaspoons water; brush loaves. Bake for 25 minutes or until golden brown and bottom sounds hollow when tapped. Place foil on tops of loaves if tops brown too quickly. Remove loaves to a wire rack and cool completely.