Whisk together the flour, salt, yeast, and sugar.
Heat the milk and butter together until the butter melts. Add the following and whisk; cold water, whole egg, egg yolk (from the second egg). Stir until lukewarm.
Add to the flour mixture. Stir with a spatula until you have a sticky dough ball.
Cover the bowl and let it rise in a warm area for 2 hours. Or until doubled.
Cover a work surface liberally with flour. Deflate the dough on the work surface. Use flour to make a slightly sticky dough. Shape into a loaf and place in a greased 9-inch x 5-inch bread pan.
Cover with oiled cling film and set in a warm place to rise for 45-60 minutes. Or until puffed and it feels light to touch. Note: If you are using a warm oven to proof the dough, check it after 30 minutes.
Preheat the oven to 425ºF.
Carefully remove the cling film from the dough. Gently brush with the reserved egg white and bake for 10 minutes.
Reduce heat to 350°F and bake an additional 27-30 minutes.