If using cornstarch, toss the cubed tofu in it for a crispy texture.
In a skillet or wok, heat sesame oil over medium-high heat. Add the tofu and cook until golden brown on all sides (about 8-10 minutes). Remove from the pan and set aside.
Sauté the Vegetables:
In the same skillet, add a bit more oil if necessary. Add minced garlic and grated ginger, sautéing for about 1 minute until fragrant.
Add broccoli, bell pepper, carrots, and mushrooms. Stir-fry for about 5-7 minutes until the vegetables are tender-crisp.
Combine and Cook:
Return the crispy tofu to the pan. Add soy sauce and stir to coat everything evenly. Cook for another 2-3 minutes until heated through.
Serve:
Serve the stir-fry hot over cooked rice or noodles. Garnish with sesame seeds and sliced green onions.