Pour water into a medium-sized bowl. Sprinkle yeast overtop and allow to bloom, about 10 minutes.
Whisk in sourdough starter, sugar and salt.
Add 2 ½ cups flour and stir to combine. If dough is wet and sticky, gradually add the final ½ cup flour until you have a rough, shaggy dough.
Turn onto a floured counter and knead until smooth. Shape into a ball.
Pour olive oil into a clean bowl. Add dough to the bowl and turn so that the whole ball of dough is coated in olive oil.
Cover dough with a plate or a tea towel and allow to rise until doubled in bulk, about 1 hour.
Set water and baking soda to boil in a large pot. Once boiling, turn water down to a rolling boil—between medium- and medium-high heat.
Turn dough onto a countertop—no need for flour—and divide into 8 equal pieces.
Roll each piece into a ball. Make a hole in each ball with your forefinger and enlarge it using your fore and middle fingers.
Place each shaped dough onto a parchment-lined baking sheet.
Slide 3 bagels at a time into the water. Boil for 1 minute 30 seconds, or 2 minutes for a chewier bagel. No need to turn the bagel in the water.
Return each bagel to the baking sheet and continue until all the bagels are boiled.
Brush each bagel with egg wash. Pour sesame seeds into a small plate. Dip each egg-washed bagel into the sesame seeds to coat the surface.
Bake at 375F until golden brown—about 30 minutes. Cool on a rack before slicing.