Combine all of the dough ingredients and knead vigorously for 10 minutes (if you're using an electric mixer) or up to 15 minutes (if you're kneading by hand). Since we're using a high-protein bread flour here, it takes a bit more effort and time to develop the gluten. The dough will be quite stiff; if you're using a mixer it will "thwap" the sides of the bowl, and hold its shape (without spreading at all) when you stop the mixer.
Place the dough in a lightly greased bowl, and set it aside to rise in a warm place until it's noticeably puffy though not necessarily doubled in bulk, 1 to 1 1/2 hours.
Make the everything bagel seasoning mix. In a small bowl combine the poppyseeds, black sesame seeds, white sesame seeds, garlic, onion, and salt. Set aside.
Lightly grease two baking sheets, or line them with parchment and grease the parchment. Transfer the dough to a work surface, and divide it into eight pieces.
Working with one piece at a time, roll it into a smooth, round ball. To do this, I bring up the bottom edges and pinch them together (almost making like a little dough purse). Then flip the dough over and give it a slight squish with the palm of my hand. Then I cup my hand and roll the dough in a circular motion until it forms a dough ball.
Place the balls on one of the prepared baking sheets. Cover the balls with plastic wrap, and let them rest for 30 minutes. They'll puff up very slightly.
While the dough is resting, prepare the water bath by heating the water, brown sugar, and granulated sugar to a very gentle boil in a large stockpot. Preheat your oven to 425°F.
Use your index finger to poke a hole through the center of each ball, then twirl the dough on your finger to stretch the hole until it's about 1 1/2" to 2" in diameter. Place six bagels on each of the baking sheets.
Transfer the bagels, four at a time if possible, to the simmering water. Increase the heat under the pan to bring the water back up to a gently simmering boil, if necessary. Cook the bagels for 1 minute, flip them over, and cook 1 minute more. Using a skimmer or strainer, remove the bagels from the water and place them back on the baking sheet. Repeat with the remaining bagels.
If adding toppings: Mix together an egg white and 1 tablespoon of water. Brush the tops of each bagel and sprinkle on the everything bagel seasoning.
Bake the bagels for 20 to 25 minutes, or until they're as deep golden brown color, turning them over about 15 minutes into the baking time (this will help them remain tall and round). Remove the bagels from the oven, and cool completely on a rack.