In the bowl of a stand mixer fitted with a hook attachment, add the sugar, yeast, bread flour, salt, and 1 ⅓ cups lukewarm water.
Knead on medium speed until dough is smooth and supple, about 8 to 10 minutes.
In the meantime, cut half of the Asiago cheese into small cubes and grate the remaining half with the large holes of a box grater, then set aside.
Transfer dough to a clean surface and knead in cubed cheese.
Place dough in a clean bowl and cover with plastic wrap. Set aside for 1 ½ to 2 hours until doubled in size.
Line a standard baking sheet with parchment paper and coat with cooking spray. Set aside.
Transfer dough to a clean surface and divide into 8 equal sections.
Use your hands to roll each section into a smooth ball.
Place balls onto prepared baking sheet, spacing at least a few inches apart.
Cover and set aside for 30 minutes until lightly puffed.
In the meantime, bring a pot with at least 3 inches of water to a simmer.
Add brown sugar and baking soda and stir to combine. Reduce heat to low.
Roll each ball into a 10-inch-long rope tapered on both ends.
Link the ends of each rope to create a ring.
Place your hand inside the ring and roll against the table to seal the seam.
Transfer all rings back to the baking sheet.
Preheat oven to 450 F.
Add a few bagels at a time to the simmering liquid.
Cook on one side for 1 minute, then flip and cook for 30 seconds. Repeat with remaining bagels, transferring them back to the baking sheet after boiling.
Brush the egg white over the bagels.
Sprinkle the bagels generously with grated cheese. Optionally sprinkle with black pepper.
Bake the bagels for 20 to 25 minutes on the center or bottom rack until they're a deep golden brown color.