Begin by pressing the tofu to remove excess moisture. Wrap the block in a clean kitchen towel and place a heavy object on top for about 15-20 minutes. Once pressed, cut the tofu into bite-sized cubes.
In a mixing bowl, add the cornstarch and a pinch of salt. Toss the tofu cubes in the cornstarch until they are evenly coated.
In a small bowl, whisk together the soy sauce, water, hoisin sauce, rice vinegar, minced garlic, and minced ginger. Set this mixture aside.
Heat 2 tablespoons of vegetable oil in a large skillet or wok over medium-high heat. Once hot, carefully add the coated tofu cubes. Cook for 5-7 minutes, turning occasionally until golden brown and crispy. Remove the tofu from the skillet and set aside.
In the same skillet, add the remaining tablespoon of oil. Add the broccoli florets and a splash of water. Stir-fry for about 4-5 minutes until the broccoli is tender but still vibrant green.
Return the crispy tofu to the skillet with the broccoli. Pour the sauce over the mixture and stir well to coat evenly. Cook for another 2-3 minutes until the sauce thickens slightly.
Drizzle the toasted sesame oil over the stir-fry and season with salt and pepper to taste. Toss everything together one last time.
Remove from heat and serve hot, garnished with chopped green onions and a sprinkle of toasted sesame seeds.