Heat the milk just until it starts to boil, then add the butter. Remove from heat and set aside. Heat 2 cups of the water to 110º. Add the yeast and sugar and let them rise in a draft free place until they are foaming and bubbly, about 15 minutes.
Combine the flour and table salt.
In a food processor, combine the milk and yeast mixtures, then gradually add the flour mixture. Add the flour as needed until a sticky dough is obtained. Place the dough in a lightly oiled bowl, then put the bowl in a warm (110º) draft free spot until the dough has doubled in bulk, about 1 hour.
Preheat the oven to 350º.
In a large pot, bring the remaining 3 quarts of water to a boil together with the kosher salt.
Knead the dough lightly, then divide into 4 ounce pieces.
Roll the pieces into cylinders about 6" long, tapering at each end. Form into circles and press the ends together. Let the bagels rise for about 15 minutes.
Place the bagels in the boiling water, top side down. Cover and simmer for 1 minute, then turn, recover and simmer for 3 minutes. Remove from water and place on a baking sheet, top side up. Brush the tops of the bagels lightly with the beaten egg white.
If desired, sprinkle the bagels with poppy seeds or sesame seeds. Bake for 20-25 minutes or until bagels are golden brown.