Begin by draining the tofu. Wrap it in a clean kitchen towel, place it on a plate, and then weigh it down with a cast-iron skillet or another heavy object. Allow it to press for at least 10 minutes, or up to 1 hour.
While the tofu is being pressed, prepare the sauce. In a medium bowl, whisk together the soy sauce, brown sugar, hoisin sauce, rice wine (or sake), vinegar, sesame oil, white pepper, garlic, ginger, 2 teaspoons of cornstarch, and ⅓ cup of water until well combined. Once the tofu has finished pressing, unwrap it and cut it into ¾ inch cubes. Transfer the tofu cubes to a medium bowl, season them with salt, and then coat them thoroughly in ¼ cup of cornstarch. Set the coated tofu aside for later use.
Heat a large cast-iron skillet over medium-high heat and add enough neutral oil to coat the bottom of the pan. Once the oil begins to shimmer, add the tofu in a single layer. Cook until one side turns golden brown and becomes crisp, approximately 3 minutes. Then, flip the tofu and cook until the other side is also golden brown and crisp, about another 3 minutes. Use a slotted spoon to remove the tofu from the skillet and transfer it to a plate.
In the same skillet, add the red bell pepper, celery, and scallions. Cook, stirring occasionally, until the red bell pepper begins to soften while retaining some crunch, and the vegetables develop a slight char, which should take about 4 minutes. Add the Sichuan peppercorns and crushed chiles and cook until fragrant, for about 1 minute. Next, add the cooked tofu and prepared sauce to the skillet, stirring to coat everything evenly. Allow the sauce to simmer and thicken for approximately 2 minutes. Finish by adding the peanuts and cilantro, give everything a final stir, then serve immediately with rice.