Combine flour, 1 Tablespoon granulated sugar, salt, and instant yeast in the bowl of a stand mixer fitted with a dough hook*. Stir to combine.
Coarsely crush or purée the blueberries in a food processor. You will need 1 cup (220g) of crushed berries.
Add the sourdough discard and crushed blueberries to the dry ingredients. With the mixer on low speed, slowly pour in the warm water. Mix until a shaggy dough forms.
Turn the dough to a work surface and knead for 4-5 minutes until a smooth dough forms. The dough should be smooth and not sticky. If needed, add more flour or water (1 Tablespoon at a time) to reach your desired 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 equal-size pieces. Using the palm of your hand, roll each piece into a smooth ball. Use your thumb to press through the center of each ball, stretching the hole to form your bagel shape. Make this hole larger than you think it should be - the dough will expand quite a bit while boiling and baking. Lightly cover the bagels with a clean dish towel or plastic wrap to rest for 20 minutes while you prepare the next step.
Preheat the oven to 425°F. Line 2 baking sheets with parchment paper and set aside. Bring a pot with 2 quarts of water and 2 Tablespoons granulated sugar to boil.
Place each bagel in the boiling water for 15-30 seconds on each side**. You can likely fit 2-3 bagels in the pot at a time, but make sure there is enough room for them to float openly. Remove the bagels from the boiling water using a slotted spoon or spatula, letting excess water drip off, and transfer to the prepared baking sheets. If needed, you can reshape the bagels a little after they've cooled.
Bake for 18-22 minutes or until golden brown. Let cool fully before slicing and serving.
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Notes
*You can make this recipe without a stand mixer. Use a large mixing bowl and wooden spoon, then knead by hand. **Boiling the bagels for less time will result in a thinner crust; boiling for a longer time will create a thicker crust.To use active sourdough starter: omit the yeast and replace the sourdough discard with active sourdough starter (200g). You will also need to adjust the rise times.To use frozen blueberries - If you're using frozen blueberries, let them thaw before coarsely crushing or puréeing the berries. This will help ensure that you're accurately feeling the water content of the dough, and also will keep your dough from getting too cold (which would greatly slow down your rise). You may find that you need to add some additional water to the recipe when using frozen berries, as they will have lost some of their water content.Note: A previous version of this recipe used whole blueberries rather than crushed or puréed blueberries. This new version allows the ability to get more blueberries (and more flavor) into the bagels, and to have a more accurate measurement on the water content of the berries.