Place the first 5 ingredients into the bread machine pan in the order listed.
Do not mix!
Insert the baking pan securely into baking unit, close lid.
Select the dough setting on bread machine and start.
When the cycle is complete, remove the dough from the pan and transfer to a lightly floured surface.
Divide the dough into 10 -12 equal portions.
Roll into balls, then using your thumbs make a hole in the center of each ball, working dough until hole is about 1 inch in diameter.
Place on a greased baking sheet.
Brush the top of each bagel with soft butter. Cover with wax paper and a dry towel. Let rise for 30 minutes.
Meanwhile, bring 3 quarts of water and 1 tablespoon sugar to a boil.
Reduce heat, lower bagels into water, as many as can fit without them touching.
Simmer the bagels for 1 minutes per side.
Drain on a paper towel, then place on a greased baking sheet.
Preheat oven to 400 ºF.
Prepare egg wash by whisking together 1 egg and 1 tablespoon water.
Brush the bagels lightly with the egg wash mixture.
Bake 400º F for 25 to 30 minutes until golden brown.