Heat your water to 110º-115ºF. Combine the water with the brown sugar, and oil and set aside.
Place your flour and instant yeast into the bowl of your stand mixer with the dough hook attached. Mix for 5 seconds to distribute the yeast.
Pour in your hot water mixture into the dry ingredients while mixing on low, just until everything is moistened.
While mixing on low, sprinkle in your salt and mix until combined.
Increase the speed to medium-high (speed 4 on a kitchenaid, speed 2 on the bosch) and mix the bagel dough for 6 minutes. If your dough is too dry, add a tablespoon or two of water until the dough sticks to the sides of the bowl. If it's too wet, sprinkle in a little flour.
Poke the dough, does it bounce back? The dough is ready to proof. You can also do the windowpane test (see blog post). If the dough isn't ready, mix for another two minutes or until the dough passes these tests .
Form the dough into a tight ball and place it into an oiled bowl. Cover and let the dough proof in a warm spot for 30-60 minutes or until it has doubled in size. (proof 90 minutes if you're using active dry yeast).
Divide your dough into 18 equal sized pieces.
Shape your bagels into a ball and then poke a hole through the center. Stretch the hole to about 2" wide and set the bagel aside to rest for 10 minutes.
Bring 8 cups of water to a boil and add in 1 teaspoon of salt and ¼ of honey or maple syrup.
Prepare two sheet pans with parchment paper. Sprinkle a good amount of corn flour (semolina) on top. This prevents the bagels from sticking.
Preheat your oven to 425ºF.
Place your bagels into the boiling water and cook for 30 seconds on each side then drain with a slotted spoon before placing onto the parchment paper.
Whisk together the egg and water. Brush all your bagels with egg wash using a pastry brush and sprinkle on your desired toppings.
Bake at 425 for 20-25 minutes or until they are golden brown.