Preheat a wok over medium-high heat for 1 minute. Add 1 tablespoon oil, swirling to coat. Season tofu with salt and cook until golden and crispy, about 5 minutes. Remove and set aside. Add 1 tablespoon oil and cook eggplant, stirring, until golden and tender, about 4 minutes. Remove and set aside. Add remaining tablespoon oil and cook ginger, garlic, and scallion whites, stirring, 1 minute. Add cabbage, kale, and 1/4 cup water and cook, stirring, until kale is tender, about 3 minutes.
Mix in rice. Once heated through, add tofu and eggplant. Stir in Sriracha and soy sauce.
Remove from heat; stir in lime juice. Garnish with scallion greens.