Sesame Noodles with Shredded Chicken

Name: Sesame Noodles with Shredded Chicken
Ingredients: 1/4 cup sesame seeds; 1/4 cup chunky peanut butter; 2 medium cloves garlic , minced or pressed through garlic press (about 2 teaspoons); 1 tablespoon minced fresh ginger; 5 tablespoons soy sauce; 2 tablespoons rice vinegar; 1 teaspoon hot pepper sauce (such as Tabasco); 2 tablespoons packed light brown sugar; water (hot); 1 1/2 pounds boneless, skinless chicken breast halves; 1 tablespoon table salt; 1 pound fresh Asian noodles or 12 ounces dried spaghetti; 2 tablespoons toasted sesame oil; 4 scallions , sliced thin on diagonal; 1 medium carrot , grated