Cook pasta in large pot of boiling salted water until tender but still firm to bite. Drain. Transfer pasta to large bowl; add 3 tablespoons sesame oil and toss to coat.
Heat remaining 1 tablespoon oil in heavy large skillet over medium-high heat. Add 6 green onions, garlic, and ginger; sauté until onions soften, about 2 minutes. Add honey, peanut butter, soy sauce, vinegar, and chili-garlic sauce; whisk to blend. Simmer sauce 1 minute. Cool to room temperature. Pour over pasta and toss to coat. Add sprouts and carrots; mix well. Transfer to platter; sprinkle with remaining green onions.