Press the tofu by wrapping in clean kitchen towels and placing something heavy on top for 15-30 minutes. Meanwhile, cook jasmine rice according to package directions.
Crumble the pressed tofu into bite-sized pieces with your hands or a fork. Set aside.
Mix the sauce by combining light soy sauce, dark soy sauce, vegetarian oyster sauce, brown sugar, and water in a small bowl. Stir until sugar dissolves.
Heat wok or large skillet over medium-high heat until nearly smoking. Add avocado oil and swirl to coat.
Add crumbled tofu in an even layer. Let sit undisturbed for 2-3 minutes until golden and crispy on the bottom. Stir and repeat once more.
Push tofu to one side. Add a bit more oil if needed, then add minced garlic, sliced chilies, and diced red onion. Stir-fry for 1 minute until fragrant.
Mix everything together and pour in the sauce mixture. Toss for 1-2 minutes until sauce coats the tofu and reduces slightly. Pan should look almost dry.
Turn off heat and immediately add Thai basil leaves. Stir until basil wilts from residual heat, about 30 seconds.
Serve immediately over cooked jasmine rice. Garnish with lime wedges and sliced scallions.