Combine the warm water and 1 Tablespoon granulated sugar in the bowl of a stand mixer fitted with a dough hook*. Sprinkle the active dry yeast on top and let sit for 5 minutes until foamy and fragrant. If your yeast does not foam, that means your yeast is dead, and you'll need to start over with fresh yeast.
Add the flour, Greek yogurt, sourdough discard and salt. Mix until combined and a rough dough forms. Transfer the dough to a smooth work surface** and knead by hand for 4-5 minutes until the dough is smooth and soft. This will be a fairly sturdy dough and should not be sticky. If needed, add more flour or water (1 Tablespoon at a time) to reach the right dough consistency.
Transfer the dough to a large, greased bowl, and cover with plastic wrap. Let the dough rise for 90 minutes, or until doubled in size.
Turn the dough out onto a smooth surface and divide into 8-10 equal pieces. 8 pieces will give you 8 large bagels; 10 pieces will give you 10 smaller bagels. Roll each piece in your palm to form a smooth ball, then use your thumb to press through the center of each ball, stretching the hole to form your bagel. Cover the bagels with 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 a pot with 2 quarts of water and 2 Tablespoons granulated sugar to boil.
Place your bagels in the boiling water for 20-30 seconds 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 and transfer to the prepared baking sheets. If needed, you can reshape the bagels a little after they've cooled.
Whisk together the egg white and 1 Tablespoon water to create the egg wash. Lightly brush the bagels with egg wash, then sprinkle with your chosen toppings (such as sesame seeds, poppy seeds, or everything bagel seasoning).
Bake for 18-22 minutes or until golden brown. Let cool fully before slicing and serving.
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Notes
Nutrition information shared is per bagel, assuming 8 bagels per batch. *You can make these bagels without a stand mixer. To do so, make the dough in a large bowl and mix with a wooden spoon, then knead by hand. **You can also knead the dough in the stand mixer, but I highly recommend kneading by hand for the best results!Passing the float test: When the bagels are added to the boiling water, they should float (called "passing the float test"). If they do not float, cover the unboiled bagels with the clean kitchen towel again and let rest for another 10 minutes. Then, try again. 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 for the recipe.