Dissolve yeast in warm milk in a large bowl. Let stand until creamy, about 10 minutes. Add egg yolk, butter, then 2 cups bread flour; stir well to combine. Stir in remaining flour, 1/2 cup at a time, beating well after each addition. When the dough has pulled together, turn it out onto a lightly floured surface and knead until smooth and elastic, about 8 minutes.
Divide the dough into 3 equal pieces and roll each piece into a 14-inch long cylinder. Braid the pieces together and place on a lightly greased baking sheet. Cover with a damp cloth and let rise until doubled in size, about 1 hour.
Meanwhile, preheat the oven to 425 degrees F (220 degrees C).
Beat together egg white and water in a small bowl. Brush risen loaf with egg wash and bake in preheated oven until golden, 20 to 25.