To prepare sauce, combine tahini and next 9 ingredients (through garlic) in a small bowl; stir with a whisk.
To prepare noodles, cook pasta in a large pot of boiling water 5 minutes, omitting salt and fat. Add broccoli to pan, and cook 1 minute. Add carrots to pan; cook 1 minute. Drain; place in a large bowl. Sprinkle with onions and remaining ingredients. Drizzle with sauce; toss well. Serve immediately.