Combine flour, 1 Tablespoon granulated sugar, chopped rosemary, yeast, and salt in the bowl of a stand mixer fitted with the dough hook attachment*. Mix to combine.Note: The remaining 2 Tablespoons of granulated sugar will be used when boiling the bagels.

Add the sourdough discard. With the mixer on low speed, slowly add the warm water and mix until combined. Increase speed to medium and mix until a shaggy dough forms. Transfer the dough to a clean work surface and knead by hand for 4-5 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), depending on your sourdough discard, to reach the right dough consistency.

Grease a large bowl, transfer the dough to the bowl, and cover with plastic wrap or a clean kitchen towel. Let the dough rise for 60-90 minutes, or until doubled in size.

Turn the dough out onto a clean work surface and divide into 8-10 equal pieces. 8 pieces will give you 8 large bagels; 10 pieces will give you 10 smaller bagels. When making 8 bagels, the dough weighs about 139g for each portion. Roll each portion of dough into a smooth ball, using one palm for friction. Use your thumbs to press through the center of each ball, stretching the hole to form your bagel. Make this hole larger than you think it should be (it will get smaller during the boiling and baking process). 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 and set aside. Bring a pot with 2 quarts of water and 2 Tablespoons granulated sugar to a boil.

Place your bagels in the boiling water for 15-30 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. Remove from the boiling water using a slotted spoon or spatula 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 the flaky sea salt.

Bake for 18-22 minutes or until golden brown, flipping and rotating the baking sheets halfway through. Let cool fully, then slice and serve.