Combine flour, granulated sugar, instant yeast and salt in the bowl of a stand mixer* fitted with the dough hook attachment. Mix to combine. On low speed, add the sourdough discard and water, mixing until a shaggy dough forms. Transfer the dough to a work surface and knead by hand for 3-4 minutes until a smooth ball forms. This will be a fairly sturdy dough and should not be sticky. You may need to add more water or more flour (1 Tablespoon at a time) to reach the right dough consistency.
Transfer the dough to a large, greased bowl. Cover with plastic wrap and let rise for 90 minutes or until doubled in size.
Turn the dough out onto a smooth work surface and divide into 10 equal-size pieces. This does not need to be exact, but I recommend using a kitchen scale to measure and divide the dough if you do want them to be exactly the same (mine were about 109g each).
Using one of your palms for friction, roll each piece of dough into a smooth ball. Use your thumb to press through the center of each ball, stretching the hole to form your bagel. Stretch this hole larger than you think it should be - the bagels will rise and expand quite a bit during boiling and baking. Cover the bagels with plastic wrap or a clean kitchen towel and let rest for 20 minutes while you prepare the next step.
Preheat oven to 425°F. Prepare 2 baking sheets lined with parchment paper or a silicone baking mat and set aside. Bring 10 cups of water and ⅔ cup baking soda to a boil in a large pot.
Place your bagels in the boiling water for 1 minute on each side. The bagels should float (if not, see notes below). You can likely fit 2-3 bagels in the pot at a time, just make sure there is enough room for them to float openly as they will expand. Remove from the boiling water using a slotted spoon or spatula, shake off excess water, and transfer to the prepared baking sheets. If needed, you can reshape the bagels a little after they've cooled.
Whisk together the egg yolk with 1 Tablespoon water to create the egg wash. Lightly brush the bagels with egg wash, then sprinkle with flaky sea salt.
Bake for 18-20 minutes or until golden brown (like a pretzel!). Let cool fully before slicing and serving.
Video
Notes
*You do not need a stand mixer to make this recipe. You can also mix the dough in a large bowl with a wooden spoon, then knead by hand. To make this recipe with active sourdough starter, omit the yeast and replace the sourdough discard with active starter (200g). You will also need to increase the rise times. Passing the float test: When you boil the bagels, they should float in the water. If your bagels do not float, cover the unboiled bagels with plastic wrap and let rise for another 10 minutes, then try again. If they are not floating, they have not risen long enough and will be dense (which is why they sink).