Place the tofu on a rimmed plate or baking dish, cover it with aluminum foil, and set a heavy pot (or other similar object) on top. Press the tofu for 30 minutes. Discard the expelled liquid. Cube the tofu.
In a medium-sized mixing bowl, whisk together the cornstarch, salt, and pepper. Toss the tofu in the cornstarch mixture until well coated.
In a small bowl, whisk together vegetable stock, soy sauce, sugar, rice vinegar, toasted sesame oil, and grated ginger. In a separate small bowl, whisk together the cornstarch and water. Whisk the cornstarch slurry into the rest of the sauce. Set aside.
Heat 2 tablespoons of refined sesame oil in a large skillet or wok over medium-high heat. Add the tofu and cook until golden brown and crispy on all sides, stirring occasionally. Remove tofu from the skillet and set aside.
Heat the remaining sesame oil in the same skillet, add minced garlic, and sauté until fragrant. Add sliced mushrooms and julienned carrots. Saute until the mushrooms turn golden brown. Stir in the snow peas, bamboo shoots, and water chestnuts. Sauté for an additional minute.
Return the tofu to the skillet and add the sauce. Give everything a good stir and cook until the sauce has thickened. Stirring frequently.
Serve warm garnished with sliced scallions.
Notes
To store: Transfer leftover moo goo gai pan to an airtight container and refrigerate for up to 3-4 days. To reheat, simply warm it in a skillet over medium heat or in the microwave.To freeze: Transfer to a freezer-safe container or freezer bag, expelling as much air as possible before sealing to prevent freezer burn. It can be stored in the freezer for up to 3 months. When you're ready to enjoy it, thaw in the refrigerator overnight, then reheat according to the instructions above.