Add the bread flour, sugar, and salt to the yeast mixture. Mix until a stiff dough forms.
Lightly oil a clean bowl with olive oil. Place the dough in the bowl, cover with a clean cloth, and let it rise in a warm spot for about 60 minutes until it's double in size.
Boil the bagels in small batches for 1 minute on each side. Remove them with a slotted spoon, place on parchment-lined baking sheets, and brush with the egg wash.