In a mixing bowl, combine the warm water and barley malt syrup (or brown sugar). Sprinkle the active yeast over the top and let it sit for about 5–10 minutes until it becomes frothy.
In a separate bowl, whisk together the bread flour and sea salt.
Once the yeast mixture is frothy, pour it into the bowl of dry ingredients. Stir with a wooden spoon or a dough scraper until a shaggy dough forms.
Turn the dough out onto a lightly floured surface and knead it for about 10 minutes, or until it becomes smooth and elastic.
Place the kneaded dough into a lightly greased bowl, cover it, and let it rise in a warm place for about 1 hour or until it doubles in size.
After the dough has risen, punch it down to release the air. Divide the dough into approximately 8-10 portions. Roll each piece into a ball and poke a hole in the center.
Place the shaped bagels on a baking sheet lined with parchment paper. Cover them lightly and let them rest for another 30 minutes while you preheat the oven.
Bring a large pot of water to a boil and add the additional 1/3 cup of barley malt syrup or brown sugar. Carefully drop in a few bagels at a time, boiling for about 30 seconds on each side.
Preheat your oven to 425°F (220°C). Bake the bagels for 20-25 minutes or until they are golden brown and sound hollow when tapped on the bottom.
Transfer the baked bagels to a cooling rack and let them cool for a few minutes before slicing.