Sesame Noodles With Shredded Chicken

1. FOR THE SAUCE: Puree 3 tablespoons sesame seeds, peanut butter, soy sauce, vinegar, sugar, ginger, garlic, and hot sauce in blender or food processor, about 30 seconds. With machine running, add hot water, 1 tablespoon at a time, until sauce has consistency of heavy cream.
2. FOR THE CHICKEN AND NOODLES: Bring 6 quarts water to boil in large pot. Position oven rack 6 inches from broiler element and heat broiler. Spray broiler pan top with vegetable oil spray, place chicken breasts on top, and broil until lightly browned, 4 to 8 minutes. Flip chicken over and continue to broil until meat registers 160 to 165 degrees, 6 to 8 minutes. Transfer to cutting board and let rest 5 minutes. Shred chicken into bite-size pieces and set aside.
3. Add noodles and salt to boiling water and cook, stirring occasionally, until tender, about 4 minutes for fresh or 10 minutes for dried. Drain, then rinse under cold water until cool. Drain again, transfer to large bowl, add sesame oil, and toss to coat. Add shredded chicken, scallions, carrot, and sauce and toss to combine. Divide among bowls, sprinkle with remaining 1 tablespoon sesame seeds, and serve.

SESAME NOODLES WITH SWEET PEPPERS AND CUCUMBERS
Omit chicken. Add 1 red bell pepper, stemmed, seeded, and sliced into 1⁄4 inch-thick strips and 1 cucumber, peeled, halved lengthwise, seeded, and cut crosswise into 1⁄8-inch-thick slices, to noodles with sauce. Sprinkle servings with 1 tablespoon chopped fresh cilantro along with sesame seeds.