In a small bowl combine the water and sugar. Stir in the yeast. Let stand until slightly foamy, about 5 minutes.
Sift together the salt and both of the flours onto parchment paper. Add to a food processor (alternatively just make dough by hand, stirring with a wooden spoon in a large bowl). Add the yeast mixture, 1 tbsp. olive oil and 7 tbsp. of Asiago cheese to the food processor. Pulse until dough just comes together. Turn out the dough onto lightly floured work surface. Knead by hand until smooth and elastic, about 10 minutes. Transfer the dough to a lightly oiled bowl and cover with plastic wrap. Let rise for 1 hour or until doubled in size.
Preheat oven to 400 degrees F. Sprinkle baking sheet with cornmeal.
Cut dough into 16 equal pieces. Roll out the pieces of dough with the palm of your hand until breadsticks are about as thick as a pencil, about 12-inches long. Place bread sticks 2-inches apart on the prepared baking sheet. Brush with beaten egg white and lightly sprinkle with cayenne pepper and remaining grated Asiago cheese. Cover breadsticks with plastic wrap and let rest for 20 minutes or until doubled in size.
Bake for 16 to 20 minutes or until golden brown and crisp. Let cool and serve.