To drain the tofu, wrap the block in a double layer of paper towels or a kitchen towel and lightly press down to squeeze out excess liquid. Cut the tofu into ½-inch cubes.
Put tofu in a bowl and toss with cornstarch to coat.
Heat 1 tablespoon oil in a nonstick pan over medium-high heat. Once hot, add the tofu in a single layer (you may need to do this in multiple batches) and cook until golden on all sides, about 3 minutes per side. Transfer to a paper towel-lined plate and set aside.
In the same pan still over medium-high heat, add 2 tablespoon oil. Add eggplant in a single layer (you may need to do this in two batches). Let eggplant sear, undisturbed, until golden brown on one side, 3-4 minutes. Stir and cook another 2 minutes until tender. Transfer to a plate and set aside.
Lower heat to medium and add bell peppers (you can add more oil if needed). Sauté for about 3 minutes, stirring occasionally, until they start to soften. Add garlic and chiles. Stir and cook for another 30 seconds, until fragrant.
In a medium bow, stir together soy sauce, oyster sauce, rice vinegar, fish sauce, brown sugar, and water.
Return tofu and eggplant to the pan and pour the sauce over it. Toss gently to coat everything in sauce and continue cooking for 1–2 minutes until sauce thickens slightly.
Remove pan from heat and stir in basil leaves.
Serve over jasmine rice and garnish with lime wedges.