Place first 5l ingredients in order listed into bread machine pan.
Do not mix!
Insert baking pan securely into baking unit, close lid.
Select dough setting on breadmaker, push start button.
When cycle is complete, remove dough from pan and transfer to lightly floured surface.
Divide dough into 10 -12 equal portions.
Roll into balls, then using thumbs make a hole in the center of each ball, working dough until hole is about 1 inch.
Place on a greased baking sheet.
Grease top of each bagel with soft butter. Cover with wax paper and 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
Simmer 1-2 minutes per side.
Drain on paper towel, then, place on greased baking sheet.
Brush lightly with egg wash. Prepare egg wash by whisking together 1egg and 1 tbsp. water.
Bake 400º F for 25 to 30 minutes until golden brown.