Place the water, eggs, butter, bread flour, sugar, yeast, and salt in your bread machine.
Select the dough cycle and hit start. Process the dough according to the manufacturer's instructions.
Transfer the dough to a bowl and cover tightly with plastic wrap. Refrigerate overnight or up to two days.
Turn the dough out onto a well-floured surface. Divide into two.
Press each half into a 4-inch round, and fold the edges into the center until a ball forms.
Turn, seam side down, and continue to form into a ball.
Spray an 8 ½” x 4 ½-inch loaf pan well.
Place the rounds, seam side down, in the loaf plan, pressing the dough into the corners.
Let rise for 2 hours. Preheat the oven to 350° F.
Beat the remaining egg with a tablespoon of water and add a pinch of salt. Brush on top of the bread.
Bake for 35 to 40 minutes, until the internal temperature is 190 degrees. Let cool in the loaf pan for 15 minutes, and then allow to cool completely on a wire rack before slicing.