Step 1: Begin by draining the extra-firm tofu. Wrap it in several layers of paper towels or a clean kitchen towel. Place it on a plate, then put another plate on top and weigh it down with something heavy (like a few cans or a book). Press for at least 15-20 minutes to remove excess water. Once pressed, cut the tofu into 1-inch cubes.
Step 2: In a medium bowl, gently toss the tofu cubes with 1 tablespoon of soy sauce, 1 tablespoon of cornstarch, and 1 teaspoon of sesame oil. Let it sit for at least 5-10 minutes while you prep your vegetables and sauce.
Step 3: In a small bowl, whisk together the remaining 3 tablespoons of soy sauce, 1 tablespoon of rice vinegar, 1 tablespoon of brown sugar (or maple syrup), 1 teaspoon of grated fresh ginger, 1 clove of minced garlic, and 1 teaspoon of sesame oil. Add 1/4 cup of vegetable broth and 1 teaspoon of cornstarch, whisking until smooth. Set aside.
Step 4: Heat 1 tablespoon of cooking oil in a large skillet or wok over medium-high heat. Once hot, add the marinated tofu in a single layer. Cook for 5-7 minutes, flipping occasionally, until all sides are golden brown and crispy. Remove the tofu from the pan and set it aside.
Step 5: Add another 1 tablespoon of cooking oil to the same skillet. Add the chopped broccoli florets, sliced carrots, and bell pepper. Stir-fry for 3-5 minutes until the vegetables are tender-crisp. Add the mushrooms and green onions (white parts) and stir-fry for another 2 minutes.
Step 6: Return the crispy tofu to the skillet with the vegetables. Give the prepared stir-fry sauce a quick whisk again (cornstarch tends to settle) and pour it over the tofu and vegetables. Stir continuously for 1-2 minutes until the sauce thickens and coats everything beautifully.
Step 7: Remove from heat. Stir in the green parts of the green onions. Garnish with toasted sesame seeds and a drizzle of extra sesame oil, if desired. Serve immediately over steamed brown rice, quinoa, or noodles.