1. Combine the Wet Ingredients: In a large mixing bowl, whisk together the unfed sourdough discard, warm water, granulated sugar (or honey), and salt until well combined. The mixture might look a little bubbly from the discard, which is perfectly normal.

2. Add the Flour and Form the Dough: Gradually add the all-purpose flour to the wet ingredients, mixing with a wooden spoon or your hands until a shaggy dough forms. Once the dough comes together, turn it out onto a lightly floured surface.

3. Knead the Dough: Knead the dough for about 8-10 minutes until it becomes smooth and elastic. It should spring back slowly when you poke it. If the dough is too sticky, add a little more flour, one tablespoon at a time.

4. First Rise (Overnight Fermentation): Place the kneaded dough in a lightly oiled bowl, turning it once to coat. Cover the bowl tightly with plastic wrap or a damp kitchen towel and refrigerate for 8-12 hours (or overnight). This slow, cold fermentation is essential for flavor development.

5. Shape the Bagels: The next morning, remove the dough from the refrigerator. Divide the dough into 8-10 equal pieces. Roll each piece into a smooth ball, then poke a hole in the center with your thumb. Gently stretch the hole to about 1-1.5 inches in diameter, creating the classic bagel shape. Place the shaped bagels on a parchment-lined baking sheet.

6. Boil the Bagels: Preheat your oven to 425 F (220 C). Bring a large pot of water to a rolling boil and add the baking soda. Carefully drop 2-3 bagels into the boiling water at a time. Boil for 30-60 seconds per side. This boiling step is crucial for the chewy texture and shiny crust.

7. Add Toppings and Bake: Using a slotted spoon, remove the boiled bagels from the water, letting excess water drain. Place them back on the parchment-lined baking sheet. If desired, sprinkle with your chosen toppings. Bake for 18-22 minutes, or until golden brown and cooked through.

8. Cool and Enjoy: Transfer the baked bagels to a wire rack to cool completely before slicing and serving. This allows the internal structure to set properly.