Combine water and yeast in a mixer bowl; let sit for 5 minutes to soften yeast. Add sugar, butter, whole egg, egg yolk, cornmeal, whole wheat flour, salt and garlic powder and beat for 2 minutes. Add 1 cup all-purpose flour and beat 2 minutes. Add enough of the remaining all-purpose flour until a soft dough forms. Knead on a lightly floured surface for 4 to 6 minutes until smooth and elastic. Place dough in a well greased bowl, turn once to coat, cover and let rise in a warm, draft-free place for 1 hour. Dough will rise, but not double.
Mix cheese, Italian seasoning and garlic powder; set aside. Punch dough down and roll into a 16 x 12-inch rectangle, about 1/4-inch thick. Drizzle with olive oil, sprinkle with cheese mixture and press gently into dough.
Cut dough in half (crosswise) using a pizza cutter or sharp knife. Cut dough into 1-inch wide strips, forming 10 breadsticks on each side of the crosswise cut. Place strips onto 2 baking sheets lined with parchment paper, about 1/2-inch apart (10 breadsticks per baking sheet). Cover and let rise 1 hour, or until doubled in height.
Bake in a preheated oven at 375°F for 9 to 12 minutes, or until golden brown. Rotate pans half way through baking. Cool slightly on wire rack. Best served warm.