Whisk TABASCO® SWEET & Spicy Sauce, chicken broth, soy sauce, and cornstarch in small bowl until cornstarch dissolves; set aside. Season chicken with salt and pepper. Heat vegetable oil in heavy large skillet over high heat.
Add garlic and ginger and stir until fragrant, about 30 seconds. Add chicken to skillet and stir-fry until white, about 2 minutes. Add broccoli florets, bell pepper, onion, and stir-fry until vegetables are crisp-tender and chicken is just cooked through, about 3 minutes.
Add chicken broth mixture and bring to boil, stirring constantly. Cook until sauce thickens, about 1 minute. Stir in chopped scallions.
Serve with rice.