Whisk the cornstarch and salt together in a shallow dish, then toss each tofu cube in the mixture until evenly coated on all sides.

Heat a thin layer of neutral oil in a large nonstick skillet over medium-high heat until the oil shimmers and bubbles slightly. Fry the tofu cubes for about 10 minutes, flipping every few minutes until they are deeply golden and crisp, then transfer to a paper towel-lined plate to drain.

Warm the sesame oil in a large pot or clay pot over medium heat while the tofu finishes frying. Sauté the ginger, garlic, and scallions for about 3 minutes until the aromatics are fragrant and the garlic just begins to color.

Increase the heat to medium-high and stir in the sliced mushrooms. Add the Shaoxing wine and cook for about 1 minute until the liquid has mostly evaporated.

Stir in the vegetable broth, soy sauce, sugar, and white pepper, then carefully add the fried tofu. Simmer for about 4 minutes until the liquid reaches a boil.

Whisk the cornstarch and water together in a small bowl to create a smooth slurry. Pour the slurry into the pot while stirring and continue to simmer for 3 minutes until the sauce turns glossy and thick.

Allow the tofu to cook for another 2 to 3 minutes to fully absorb the savory sauce. Serve hot with steamed rice.