Set the tofu cubes on a paper towel-lined plate while you prepare the remaining ingredients. Handle the tofu gently so the cubes stay intact.
Heat the oil in a large skillet or wok over medium-high heat. Add the chopped shiitake mushrooms and cook, stirring often, until they release their moisture and begin to brown, about 4 minutes.
Add the doubanjiang, garlic, ginger, scallion whites, and ground Sichuan peppercorns. Stir constantly for about 30 seconds, until fragrant; do not let the garlic scorch.
Pour in the Shaoxing wine, soy sauce, vegetable broth, and sugar. Bring the sauce to a gentle simmer, scraping up any flavorful bits from the skillet.
Stir the cornstarch slurry again, then slowly pour it into the simmering sauce while stirring. Cook for 1 minute, until the sauce looks lightly glossy and thickened.
Slide in the tofu cubes. Spoon sauce over the tofu and simmer gently, without vigorous stirring, until heated through, about 3 to 4 minutes.
Taste and add a little more ground Sichuan peppercorn if you would like more numbing citrus-like warmth. Scatter with the scallion greens and serve immediately with steamed rice, if desired.