Cook soba noodles in boiling water for about 5 minutes. Strain, rinse, toss with a bit of sesame oil, and set aside. Cut chicken into small strips and toss with ginger, garlic, salt, and pepper. Heat remaining sesame oil in a wok or large skillet. Once the oil is hot, add the chicken and cook for 5-6 minutes, or until no longer pink. Add the bell pepper and broccoli and cook for an additional 2-3 minutes. Add the scallions and the Szechuan sauce and cook an additional minute. Toss the chicken and veggies with the noodles and serve.