In a large bowl or stand mixer, stir together yeast, flour, salt, brown sugar, and warm water. Mix until a firm dough forms.
Knead by hand on a lightly floured surface or with the mixer’s dough hook for 8–10 minutes until the dough is smooth and elastic.
Lightly oil a bowl, place the dough inside, cover, and let rise in a warm spot for 1–1½ hours, until noticeably puffy.
Turn the dough out, divide into eight equal pieces (about 4 oz. each), and roll into tight balls. Rest 20 minutes to relax the gluten.
Poke a hole through each ball’s center with your thumb, then gently stretch to a 1½–2″ ring. Place on parchment-lined baking sheets.
Preheat oven to 425°F (220°C). Meanwhile, bring 2–3 quarts of water, brown sugar, and granulated sugar (or honey) to a simmer in a wide pot.
Boil 3–4 bagels at a time for 1 minute per side, gently turning once. Drain on a wire rack.
Whisk egg white and water, brush each bagel top and sides, and sprinkle with chosen toppings.
Bake 20–25 minutes until glossy and golden. Transfer to a cooling rack immediately to avoid sticking.
