In a bowl, combine the warm water, sourdough discard, and honey or sugar. Add the bread flour, yeast, and salt, and mix until a stiff dough forms.
Knead the dough for 8–10 minutes, either by hand or in a stand mixer, until smooth and strong. The dough should feel firm and not sticky.
Cover the dough and let it rise for 60–90 minutes, until slightly puffy but not doubled in size.
Divide the dough into 8 equal pieces, about 100–105g each. Roll each piece into a tight ball and let them rest for 20 minutes. Poke a hole in the center of each ball and stretch into a bagel shape.
Place the shaped bagels on a parchment-lined tray, cover, and let rest for 30–45 minutes, until slightly puffy.
Bring the water, honey or brown sugar, and baking soda to a boil. Boil the bagels for 30–60 seconds per side.
Bake at 425°F (220°C) for 20–25 minutes, until deep golden.