In the bowl of an electric mixer or a regular large mixing bowl, mix the bread flour, yeast, salt, and brown sugar. Add the egg yolks, eggs, and water and mix on low speed until a dough begins to form.
Cover the bowl with plastic wrap and place in a warm location for about 1 hour or until the mixture becomes foamy and has doubled in size.
Using the dough hook, beat the dough on low speed for about 7 minutes or 10 minutes by hand until the dough is smooth and workable. If the dough is too sticky, add additional flour, 1 tablespoon at a time.
Divide the dough into 8 equal pieces and roll each into a ball. Place the dough balls on a large plate or baking sheet and cover them with a damp towel. Set aside to rest for 15-20 minutes.
To shape the bagels, use your thumb to poke a hole in the center of the dough. Stretch the dough with your thumb to widen the hole. Repeat with the remaining dough balls.
Place the bagels on a lined baking sheet and cover them with plastic wrap. Set aside to rest for 10-15 minutes.
Position the rack in the center of the oven and preheat to 450°F.
Bring a large pot of water to a boil. When the water is boiling, add the baking soda and adjust the water to a low boil. Gently drop the bagels into the water and boil for 1 minute. Flip the bagels and boil for another minute.
Line a baking sheet with parchment paper and dust with cornmeal if desired.
Remove the bagels from the water with a slotted spoon and transfer them to the baking sheet.
If using egg wash, whisk an egg and brush some of the beaten egg on top of each bagel. Sprinkle with poppy seeds or everything bagel seasoning if desired.
Bake for 15-17 minutes, rotating the baking sheet halfway through until the bagels are golden brown.
Transfer the bagels to a wire rack to cool.
Serve and enjoy!