Mix 2 cups flour and yeast together in the bowl of a stand mixer.
Stir milk, butter, sugar, and salt together in a saucepan; heat and stir over medium-low heat until the mixture is smooth and the temperature is between 90 degrees F (32 degrees C) to 100 degrees F (37 degrees C).
Pour the milk mixture into the flour mixture, add eggs, and beat on low speed for 30 seconds. Increase speed to high and beat for 3 minutes more. Add 1 cup flour and 3 tablespoons orange juice to the mixture; mix on high for 3 minutes more.
Fit the mixer with a dough hook. Add remaining flour to the mixture; beat with dough hook until the flour is completely incorporated.
Grease a glass bowl. Put dough into the bowl. Let dough rise until doubled in volume, 1 to 2 hours.
Preheat oven to 350 degrees F (175 degrees C).
Punch dough down. Divide the dough into two halves. Split each half into three even pieces, roll each piece into a cylinder, and braid into loaves. Put loaves onto a baking sheet. Let rise, about 1 hour.
Bake in preheated oven until the middle is baked, 25 to 30 minutes.
Stir confectioners’ sugar and 1 tablespoon orange juice together in a bowl; brush onto the tops of the loaves.