Combine all the ingredients for the dough in a big mixing bowl and stir with a sturdy spoon until a shaggy dough comes together (alternately you can use a stand mixer with a dough hook if one is available to you.) Turn out onto a clean surface and knead until smooth and elastic. The dough should be quite a stiff dough, that's okay. Place in a greased bowl, cover with a damp towel or plastic wrap, and let rise in a warm, draft-free place until doubled in bulk.

Turn the dough out onto a work surface and divide into 8 equally sized pieces. Roll each piece into a smooth ball. This is easiest to do if you roll it around on the countertop in a repetitive circular pattern with your hand cupped gently over it. Let the dough balls rest, covered with a clean towel, for 30 minutes.

Preheat oven to 450°F.

Make the bagel boil by combining the water, baking soda, and brown sugar in a wide, deep pan. Bring to a boil and lower the heat to a simmer.

Poke your index finger down through the center of each dough ball to the counter. Pick the dough ball up and gently stretch the hole you made until it is about 2 inches in diameter. Take care not to deflate the dough too much. Place it back on the counter and repeat with the remaining dough.

Once they're all done, lower one bagel at a time into the water (lowering the side that was facing up on the countertop into the water first.) Do not overcrowd the pan. Each batch for boiling should be no larger than 4 bagels. Boil those 4 bagels for 2 minutes on the first side, carefully flip the bagels and boil the second side for 2 minutes. Use a slotted spoon to transfer the bagels to a silpat lined baking sheet (this will keep it from adhering to the pan as they bake). They will not expand greatly while they bake, but should still have a little space between them to allow heat to circulate well. Repeat with the remaining bagels.

Brush with the beaten egg or flax egg mixture, sprinkle generously with salt, slash the tops with a sharp knife a couple of times to a depth of about 1/8-inch. Bake the bagels until they are a deep brown colour, about 18 minutes. If you have leftovers, they store best in a paper bag that is not completely sealed. They're best eaten the day they're made, but good toasted the day after!