Pour warm water into the bowl of your stand mixer, add granulated sugar and stir to dissolve. Sprinkle instant yeast over the surface and let sit for 5 minutes until foamy.
Add the sourdough discard to the yeast mixture and stir well until fully dissolved with no lumps remaining.
Add bread flour and fine sea salt to the bowl. Mix with dough hook on low for 2 minutes until shaggy, then increase to medium and knead for 8-10 minutes until smooth, stiff, and slightly tacky but not sticky.
Shape the dough into a smooth ball and place in a lightly oiled bowl. Cover with plastic wrap or a damp towel and let rise at room temperature for 1 to 1.5 hours until doubled in size.
Turn risen dough onto a lightly floured surface and divide into 8 equal portions of about 95-100g each using a bench scraper or knife.
Roll each portion into a smooth ball, then poke your finger through the center to create a hole and stretch it to about 1.5 to 2 inches in diameter. Place on a parchment-lined baking sheet.
Cover shaped bagels loosely with plastic wrap and let them rest for 20 to 30 minutes at room temperature until slightly puffy. Perform a float test if desired.
Preheat oven to 425°F (220°C). Fill a large pot with 4 inches of water and bring to a rolling boil. Add honey and baking soda and stir briefly.
Using a slotted spoon, lower 2-3 bagels at a time into boiling water. Boil for 45 seconds per side, then remove and drain briefly on the baking sheet.
Brush each boiled bagel generously with beaten egg and immediately sprinkle with chosen toppings, pressing gently to adhere.
Bake for 20-25 minutes until deep golden brown and hollow-sounding when tapped. Let cool on baking sheet for at least 10 minutes before slicing.