Line a large plate with a double layer of paper towels. Place the tofu on the paper towels and cover with additional paper towels. Top with a small cutting board or other flat surface, then place cans or jars on top to weigh it down. Let stand 1 hour.

Meanwhile, in a blender, combine the coconut milk, sugar, garlic, lemon grass, the chopped chilies, chopped shallots, lime leaves or zest, ½ teaspoon salt and ¼ teaspoon pepper. Process until smooth, about 2 minutes; set aside.

Uncover the tofu and transfer to a cutting board. Cut the block into ½-inch-thick planks. Stack a few planks and cut crosswise into ½-inch sticks. In a wide, shallow dish or medium bowl, stir together the cornstarch, turmeric and ¼ teaspoon each salt and pepper. Add the tofu and toss until evenly coated.

In a 12- to 14-inch wok or a 12-inch skillet over medium-high, heat the oil until shimmering. Add the tofu in an even layer; cook without stirring until the tofu releases easily from the pan, about 3 minutes. Toss and cook, stirring intermittently, until crisp and golden brown, another 5 to 7 minutes. Using a slotted spoon or spatula, transfer to a plate. Pour off and discard all but 1 tablespoon of the oil.

Return the pan to medium-high, add the peanuts, sliced shallots and sliced chilies; cook, stirring, until lightly browned, 1 to 2 minutes. Transfer to another plate. To the now-empty pan, add the chili puree and cook, stirring, until thick and jammy, 3 to 4 minutes. Stir in the lime juice, kecap manis and ½ teaspoon black pepper. Return the tofu and peanut mixture to the pan. Stir, then cook without stirring, until the tofu caramelizes in spots, 1 to 2 minutes. Stir once again to combine. Off heat, taste and season with salt and pepper. Serve with lime wedges.