Preheat oven to 400 degrees. Combine the scalded milk, butter, sugar and salt. Warm gently to a temperature of between 105 degrees and 115 degrees. Remove from the heat and add and dissolve the yeast in the mixture. Wait 3 minutes while the yeast works. Blend in the eggs and flour. Knead this soft dough for 10 minutes, adding flour if needed to make it firm enough to handle. Place in a greased bowl, cover and let rise until doubled in bulk. Punch down and divide into equal parts (one part for each finished bagel). Roll each piece into a rope about 7" long and tapered at the ends. Wet the ends and form a doughnut-shaped ring from each rope. Cover and let rise on a floured board for about 15 minutes. Place in a refrigerator for 2 hours to firm up the dough. Bring the water to a boil and add the sugar. Drop the rings, one at a time, into the boiling sugar water. When the bagels surface, turn them over and cook an additional 3 minutes. Skim the bagels out of the water and place on an ungreased baking sheet. Coat each with beaten egg white. Bake in the oven until golden brown (The longer you bake, the crisper the bagel).