In a large bowl, mix the starter, water, syrup, and salt until a slurry forms.
Add the flour and mix with your hands until it is fully incorporated. The dough will be stiff but workable. Rest covered for about 10 minutes.
Remove the dough from the bowl and knead on a clean work surface for at least 5 minutes to develop dough strength.
Clean and lightly grease the bowl with oil and return the dough, rolling it to coat. Cover and bulk ferment until slightly puffy, about 3 hours.
After bulk fermentation, place the bowl in the refrigerator and retard the dough for up to 24 hours, or overnight.
Line a baking sheet with parchment paper and lightly sprinkle it with cornmeal.
Divide the dough into 12 pieces, each about 100 grams.
Pat each piece into a rough 4x2-inch rectangle. Roll and fold each rectangle tightly from the top down.
Let the pre-shaped pieces rest while you work on the remaining dough.
Roll each piece into a 10-inch coil and shape into a circle with a 2-inch hole in the center.
Place the bagels on the prepared baking sheet, leaving at least 2 inches between each.
Cover the bagels with a dry towel and place the baking sheet inside a clean plastic garbage bag. Let proof at room temperature for about 3 hours.
Preheat the oven to 475°F (246°C). Prepare your workspace with a wire rack inside a baking sheet.
In a large pot, mix about 5 quarts of water with barley malt syrup and bring to a rolling boil.
Carefully drop 3 to 4 proofed bagels into the boiling water and boil for 1 minute. For extra-chewy bagels, boil for an additional minute.
Use a slotted spoon to remove the bagels and place them on the wire rack to drain. Let them cool for about 1 minute.
If using seeds, dredge each bagel in the seeds.
Place the bagels on the parchment-lined baking sheets, leaving at least 2 inches between each one.
Bake for about 20 minutes, rotating halfway, until golden brown. Cool on a wire rack and serve immediately.
