Combine the bread flour, yeast, salt, and brown sugar in an electric mixer bowl (or a regular large mixing bowl). Mix in the eggs, egg yolks, and water on low speed until the dough forms a bowl.
Cover with plastic wrap and set aside in a warm place for 1 hour, or until the mixture foams and doubles in size.
Reattach the dough bowl to the electric mixer and continue to mix on low speed for 7 minutes (or 10 minutes without an electric mixer), or until the dough is smooth and pliable.
Roll the bagel dough into 8 equal parts and shape into a ball. Place the dough balls on a large plate or baking sheet, cover with a damp towel, and set aside for 15-20 minutes.
Poke a hole in the center of the dough with your thumb and stretch the dough by rotating your thumb to widen the hole. Repeat with the rest of the dough balls.
Place the shaped bagel doughs on a baking sheet lined with parchment paper. Wrap in plastic wrap and set aside for another 10-15 minutes.
Meanwhile, preheat the oven to 450°F and position the rack in the center.
A large pot of water should be brought to a boil. Dissolve the baking soda in the boiling water and return to a low boil. Boil for 1 minute after gently dropping the bagel doughs into the water. Boil for another minute after flipping the bagels. Transfer the bagels to a lined baking sheet dusted with cornmeal using a slotted spoon.
1 extra egg, whisked together, should be brushed onto the tops of each bagel. Poppy seeds or Everythingseasoning can be sprinkled on top.
Bake the bagels for 15-17 minutes, rotating the baking sheet halfway through, or until golden brown.
Remove the baking sheet from the oven and cool the bagels on a wire rack.
Video
Notes
If your dough remains sticky, add more flour (1 tablespoon at a time). Add more water if your dough is too dry (1 tablespoon at a time).