In medium bowl, wisk all sauce ingredients together: water, soy sauce, hoisin, rice vinegar, ginger, and 1 tbsp of chili garlic sauce. Taste and add additional garlic chili sauce if you prefer more heat.
Heat oil in large nonstick skillet or wok over medium heat. Add the broccoli and bell peppers Cook 2 minutes, then stir in the garlic, white parts of green onions, and chickpeas. Cook for and 3 additional minutes, until the vegetables are crisp tender, then pour in the sauce. Bring to a simmer and cook until the sauce thickens, about 2 minutes. Sprinkle green portion of green onions and sesame seeds. Serve hot over rice.