Mix the flour, warm water, yeast, sugar, and salt until no dry flour remains. Rest the dough for 20 minutes.
Knead on low speed for 8 to 10 minutes, or by hand for 15 to 20 minutes, until smooth and elastic. Cover and let rise in a warm place for 1 to 1 1/2 hours, until 75 percent larger.
Divide the dough into 8 equal pieces. Shape each into a tight ball, rest for 10 minutes, then make a hole through the center and stretch it to form a bagel.
Cover the shaped bagels and proof for about 30 minutes, or refrigerate for up to 24 hours for an overnight cold proof.
Bring the poaching water, honey, and baking soda to a gentle boil. Poach each bagel for 1 minute per side, then drain.
Whisk the egg white with the water. Brush the bagels, add toppings if using, and bake at 425°F (220°C), or 400°F (200°C fan), for about 20 minutes until deeply golden.