Bring water to a simmer in a skillet over medium heat; add broccoli, water chestnuts, carrots, celery, snow peas, and ginger. Simmer until vegetables are just tender, 6 to 8 minutes. Drain any remaining water.
Mix garlic into vegetable mixture; cook and stir until fragrant, about 3 minutes. Season with soy sauce and sesame oil, cooking until liquid has evaporated, about 5 minutes. Stir in toasted sesame seeds.
Sprinkle black sesame seeds over vegetables before serving.