Shred the Tofu: Use the large side of a box grater to coarsely shred the tofu. Lay the shredded tofu on a clean kitchen towel to soak up any excess moisture.
Prepare the Brussels Sprouts: Cut the Brussels sprouts in half lengthwise through their stems, then slice them thinly.
Mix the Sauce: Combine the lime zest, lime juice, brown sugar, fish sauce, and soy sauce in a small bowl. Whisk until the mixture is well blended.
Cook the Vegetables and Tofu: Heat the peanut oil in a skillet over medium-high heat. Add the Brussels sprouts, garlic, and red chile, and cook for 3 to 5 minutes, stirring frequently, until the Brussels sprouts are softened. Add the shredded tofu to the pan and stir for about 2 minutes, letting it warm through. Pour in the sauce and sprinkle in ¼ teaspoon of salt. Cook for another minute to allow the flavors to meld.
Add the Final Touches: Remove the skillet from heat and stir in the chopped peanuts, scallions, and torn basil leaves. Taste the dish and adjust the seasoning with additional salt or lime juice, if needed. Serve immediately and enjoy.