Combine the water, milk, yeast, sugar, and 1 cup of flour; stir to form a batter. Allow to ferment for 1 hour. Stir in the 2 large eggs and melted butter, then add the remaining 2 cups of flour along with the salt. Mix then knead the dough for 10-12 minutes. Place the dough in a bowl at room temperature, cover it with plastic wrap, and allow it to ferment for 1 - 1 1/2 hours.
Cut the dough into 3 equal pieces. Roll each piece of dough into 10-inch lengths and braid the bread. Place the braided loaf onto a baking sheet that has been dusted withcornmeal. Cover the bread loosely with a towel and allow it to rise for about an hour. Pre-heat an oven to 350F.
Brush the bread with the beaten egg and sprinkle it with poppy seeds. Bake the bread for about 30 minutes. Remove the Challah from the oven and place it on a wire rack or towel to cool before slicing.