Bring a large pot of water to a boil over high heat.
Add the pasta and cook according to package directions. Drain in a colander and rinse under cold water until cool.
Transfer the pasta to a large bowl, and toss with 1 tablespoon of the sesame oil.
In a food processor, add the garlic, remaining 5 tablespoons sesame oil, peanut butter, soy sauce, ginger, vinegar, brown sugar, and 1½ teaspoons salt. Process until smooth, about 30 seconds. Set aside.
Season the tenders with ¾ teaspoon salt and ½ teaspoon pepper. Heat the peanut oil in a 12-inch skillet over medium-high heat. Cook the tenders until golden brown on both sides and cooked through, about 3 minutes per side.
Place the chicken on a cutting board and slice crosswise into ½-inch pieces. Add the chicken and half the scallions to the pasta.
Pour about 1¾ cups of the dressing over the pasta and chicken and toss to coat. Add more dressing if needed. (You might not use it all.)
Transfer to a serving platter, sprinkle with the remaining scallions, and serve.