Bring a large pot of salted water to boiling. Add green beans; return to boiling. Boil 4 minutes. Add carrots; boil 1 minute more. Drain well.
In a small bowl stir together next 5 ingredients (through sesame oil); set aside.
In a large wok or a 12-inch nonstick skillet heat canola oil over medium-high heat. Add mushrooms, ginger, and garlic; cook and stir about 3 minutes or until mushrooms are tender. Stir broth mixture and add to skillet; cook and stir about 1 minute or until just thickened and bubbly. Stir in green beans and carrots and the 2 Tbsp. basil; heat through.
To serve, sprinkle with toasted sesame seeds and garnish with additional fresh basil leaves.