Combine yeast and warm water in a 2-cup liquid measuring cup; let stand 5 minutes. Combine yeast mixture, olive oil, honey, and 1 teaspoon salt in a large mixing bowl; beat at medium speed of an electric mixer until well blended. Add 2 cups flour; beat 2 minutes at medium speed. Stir in Parmesan cheese and pepper. Gradually stir in enough of the remaining 2 1/4 cups flour to make a soft dough.
Sprinkle 2 tablespoons flour evenly over work surface. Turn dough out onto floured surface, and knead until smooth and elastic (about 8 to 10 minutes). Place dough in a large, well-greased bowl, turning to grease top. Cover and let rise in a warm place (85°), free from drafts, 1 hour or until doubled in bulk.
Punch dough down, and divide into 12 equal portions; roll each portion into a 10-inch rope. Place ropes 1 inch apart on a large greased baking sheet. Brush breadsticks with egg white, and sprinkle evenly with kosher salt. Bake at 425° for 10 to 12 minutes or until golden. Remove from baking sheet, and let cool on a wire rack.