Makes: about 16 breadsticks for $1.91. Prep: 25 minutes. Rise: about 2 hours. Bake: at 425 F for 12 to 15 minutes.
Stir honey into 1/4 cup warm water in small bowl. Sprinkle with yeast. Let stand until foamy, 5 to 10 minutes.
Combine bread and all-purpose flours, sugar, salt and 1/4 cup toasted sesame seeds in large bowl. Stir in yeast mixture, remaining 3/4 cup warm water and sesame oil. Stir until dough pulls away from sides of bowl.
Turn dough out onto lightly floured surface. Knead dough until smooth and elastic, 8 to 10 minutes, adding more flour as needed to prevent dough from sticking. Place dough in greased bowl, turning to coat. Cover with clean kitchen towel or plastic wrap. Let rise in warm place until doubled in volume, 45 minutes to 1 hour.
Punch dough down. Let rest 5 minutes. On lightly floured surface, roll dough into 16 x 9-inch rectangle. Using a pizza cutter or sharp knife and beginning at a long side, cut dough into sixteen 1-inch-wide strips. Dust 2 baking sheets with cornmeal. Transfer breadsticks to pans.
Brush sticks with egg white. Sprinkle with salt and sesame seeds. Cover with clean dish towel. Let rise until doubled in volume, 45 minutes to 1 hour.
Heat oven to 425°F. Bake breadsticks for 12 to 15 minutes or until golden and hard on outside. Serve warm.