Combine bread flour, sugar, salt, and yeast in a stand mixer bowl or large mixing bowl, then add warm water (110–115°F) and mix until a shaggy dough forms with no dry flour pockets.
Knead on medium speed or by hand on a lightly floured surface for 8–10 minutes, until the dough is smooth, elastic, and springs back when poked.
Place the dough in a lightly oiled bowl, turn to coat, cover with a damp towel or plastic wrap, and let rise in a warm, draft-free spot for 1–2 hours until doubled in size.
Punch down the risen dough, turn it out onto a clean surface, and divide into 8 equal pieces (about 110–115g each) using a bench scraper or knife.
Roll each piece into a tight ball, poke a hole through the center with your finger, and gently stretch the hole to 1–2 inches wide; place on a parchment-lined baking sheet spaced 2 inches apart.
Cover the shaped bagels loosely with a kitchen towel and let rest for 10–15 minutes while you preheat the oven to 425°F (220°C).
Bring a large pot with about 3 quarts of water to a rolling boil over high heat, then stir in the barley malt syrup until dissolved.
Boil 2–3 bagels at a time for 30 seconds per side, then remove with a slotted spoon, drain, and return to the parchment-lined baking sheet; repeat with remaining bagels.
Brush the tops of the boiled bagels lightly with water, then immediately sprinkle on your chosen toppings while the surface is still wet.
Bake on the middle rack for 20–25 minutes until deep golden brown; the bagels should sound hollow when tapped on the bottom.
Transfer bagels immediately to a cooling rack and let cool for at least 10 minutes before slicing to allow the interior to set properly.