In a large bowl, combine the flour, yeast, and salt. Set aside.
In a 4-cup (1 liter) measuring cup, whisk together the eggs, brown rice syrup, and vegetable oil.
Add enough warm water to make 4 cups (1 liter) and stir with a whisk to combine well.
Pour the liquid ingredients over the flour and stir until it is moist.
Run your hand over the sides of the bowl and fold the dough towards the center 40 times.
The dough will be sticky.
Cover the bowl with plastic wrap and let the dough rise at room temperature (72 F/22 C), away from drafts, for 2 hours, until it has almost reached the top of the bowl and has the texture of a sponge.
After 2 hours, either shape your bagels to bake them, or reserve your dough in the refrigerator for up to 3 days.
Shaping:
Place the dough on a floured surface and sprinkle with a little flour.
Divide the dough into 16 equal portions.
Shape the dough into balls, then pierce the center with your thumbs.
Stretch and enlarge the central hole by rolling between your hands.
Place your bagels on baking sheets lined with parchment paper, leaving 2 inches (5 cm) of space between them.
Cover with damp cloths and let rise at room temperature for 1.5 hours.
Boiling and baking:
Preheat the oven to 450 F (230 C) and place a rack at the bottom with a drip pan filled with water.
Heat the water with the brown rice syrup.
Using a slotted spoon, carefully place the bagels in the water and poach for 20 seconds on each side.
Drain and return the bagels to the prepared baking sheets, still leaving space between them.
Liberally sprinkle the bagels with sesame seeds.
Bake the bagels for 17 to 20 minutes, or until they are golden brown.
Remove from the oven and let cool on a rack.