Nix the sourdough starter, water, olive oil, flour, and salt together by hand. This will be a firmer dough than usual. Let it rest for about 10 minutes,
Knead the dough in a mixer with a dough hook. until firm. This will be a firmer dough than usual.
Lightly grease a bowl and transfer dough. Let it rise for 4 hours.
Pour the dough on a floured work space and knead the dough by hand. After a good kneading, cut the dough into 200 grams a piece.
Shape the bagels by making each piece into a ball and using your thumb to punch a hole through the middle of the ball, stretching to make the center hole. Set the shaped bagels on a parchment or silicone lined baking sheet.
Cover and let stand for an hour.
Fill a large pot about half way with water. Add a tablespoon of baking soda and bring to a rapid boil.
Place as many bagels that would comfortably fit floating in the boiling water. Boil for 30 seconds per side. Take out and place on rack and boil another batch until done.
OPTIONAL: Bruch the bagels with the egg to glaze the top. Then sprinkle the topping of your choice. This is only limited by your imagination. Go CRAZY!
Brush the bagels with milk or an egg glaze at this point, if you wish, and top with your desired toppings.
Preheat oven to 230C. The bagel will not expand any further so you can fill the baking sheet tight, but not touching. Bake for 14 to 15 minutes or until golden brown. Cool on a rack.