Make the marinade: Whisk 2 tablespoons cornstarch, the rice wine, oyster sauce and 2 tablespoons water in a large bowl. Cut the tofu in half horizontally to make 2 large rectangles, then cut each rectangle into 4 squares. Add to the marinade and turn to coat.
Cook the peanuts in the peanut oil in a large skillet over medium heat, stirring, until lightly golden, 4 to 5 minutes. Remove the skillet from the heat and transfer the nuts to a bowl with a slotted spoon.
Drain the tofu, reserving the marinade; sprinkle both sides with the remaining 4 tablespoons cornstarch. Return the skillet to medium-high heat; add the tofu and cook until golden, 4 minutes per side. Remove to a plate. Add the ginger, garlic, chiles and 1 teaspoon salt to the skillet; stir-fry 30 seconds. Add the mushrooms and snap peas; stir-fry until crisp-tender. Whisk the marinade with 1 1/2 cups water, add to the skillet and stir until thick, 2 to 3 minutes. Add the tofu and nuts and heat through. If using dried chiles, remove before serving.