In a small bowl, sprinkle yeast over warm water. Let sit for a minute before stirring to combine. Let sit until frothy, about 10 minutes.
In the bowl of a large food processor fitted with a dough blade, combine flour, Asiago cheese, salt, 2 tablespoons sugar, and water with yeast. Process until a smooth dough forms.
Lightly oil a large bowl and add dough. Cover and let rise until doubled, about 1 hour.
Divide dough into 8 equal pieces. Roll one piece into a ball. Use your thumb to make a hole in the center and stretch to widen the hole. Repeat with remaining pieces, cover with wet towel, and let rise for 30 minutes.
Preheat oven to 375 degrees F. Bring a large pot of water to a boil and add remaining 3 tablespoons sugar. Boil bagels, about 2 at a time- careful not to overcrowd, for 30 seconds per side. Remove with large slotted spoon onto a dry towel.
Sprinkle cornmeal on a large baking sheet. Place boiled bagels on baking sheet. Brush each bagel with egg white and sprinkle with Asiago cheese. Bake in preheated oven until golden brown on top, 20-25 minutes. Remove to wire rack to let cool.