Cook the 8 oz dried linguine or rice noodles in a large pot of boiling, salted water according to package instructions.
Drain the noodles and immediately rinse under cold running water until completely cooled. Toss the cooled noodles with 1 tablespoon of the toasted sesame oil to prevent sticking.
In a medium mixing bowl, whisk together the 3 tbsp tahini, remaining 1 tablespoon of toasted sesame oil, 3 tbsp soy sauce, 1 tbsp rice vinegar, 1 tbsp granulated sugar, and 1 tsp minced garlic.
Gradually whisk the 1/4 cup hot water into the tahini mixture until the dressing reaches a smooth, creamy consistency.
In a large serving bowl, combine the cooled noodles, 2 cups cooked shredded chicken breast, 1 cup julienned cucumber, and 1 cup shredded carrots.
Pour the tahini dressing over the noodle and chicken mixture, tossing thoroughly until all ingredients are evenly coated.
Garnish the dish with 2 tbsp sliced green onions and 1 tbsp sesame seeds. Serve chilled or at room temperature.