Spread the tofu over a paper towel–lined baking sheet and let it drain for 20 minutes, then gently press dry with more paper towels. Season the tofu with salt and pepper.

While the tofu drains, process half of the basil, the garlic, and the chiles in a food processor until finely chopped. Transfer a tablespoon of this mixture to a small bowl and stir in the fish sauce, oyster sauce, sugar, and vinegar to make the sauce, then place the remaining basil mixture into a 12-inch nonstick skillet.

Pulse the tofu in the empty food processor until coarsely chopped into a crumble, about 3 to 4 pulses. Spread the tofu over fresh paper towels and press again—removing as much moisture as possible is essential for getting the tofu to brown rather than steam.

Stir the dried tofu, shallots, and oil into the skillet with the basil mixture and cook over medium heat. Stir occasionally until the tofu and shallots are well-browned and fragrant, about 10 to 15 minutes; the mixture should begin to sizzle steadily after the first minute.

Add the reserved sauce mixture to the skillet and cook, stirring constantly, until the tofu is evenly coated and the liquid has mostly evaporated, about 1 minute. Fold in the remaining basil and cook until the leaves are just wilted, then remove from the heat and stir in the peanuts.

Transfer the tofu to a platter and serve warm inside lettuce leaves, with pepper flakes and extra vinegar on the side.