Preheat the oven to 425°F (218°C). Remove the tofu from its packaging and discard any liquid. Slice it lengthwise into three slabs, then press using a lint-free paper towel or clean dishcloth to remove excess moisture. Place a heavy object, like a skillet, on top and let it press for at least 30 minutes, replacing the towel if soaked.
Cut the pressed tofu into cubes and transfer to a mixing bowl. Add 1 tablespoon of soy sauce (or tamari) and 2 tablespoons of cornstarch (or nutritional yeast). Toss to coat evenly, then spread the tofu on a baking sheet. Bake for 30 minutes, flipping halfway through, until golden brown and crispy. Set aside.
In a small bowl, whisk together ¼ cup soy sauce, 2 tablespoons water, 1 tablespoon maple syrup (or sugar), 1 teaspoon grated ginger, 1 teaspoon minced garlic, and 1 teaspoon cornstarch. Set aside. (Complete this step while baking the tofu.)
Heat the cooking oil and sesame oil in a large pan or wok over medium-high heat. Add the broccoli, carrots, and onion, tossing frequently for 2–4 minutes until slightly tender.
Add the baked tofu and the ginger garlic sauce to the pan. Stir to coat evenly, cooking for another 2–3 minutes until everything is well combined and heated through.
Remove from heat and garnish with sliced green onions and toasted sesame seeds. Serve hot with fresh rice. Enjoy!