Place tofu on a paper towel-lined plate. Cover with another paper towel and place a heavy pot on top. Allow to sit until extra moisture has released into the paper towels, about 30 minutes.
Heat peanut oil over medium-high heat in a large skillet. Add tofu, onion, and garlic and saute until onions are soft, about 5 minutes, adding water if tofu sticks to the pan. Add eggplant, cover, and cook until eggplant starts to soften, 5 to 7 minutes. Add soy sauce and chili sauce, lower heat to medium, and continue cooking until eggplant becomes translucent, 7 to 10 minutes. Add basil and stir until wilted, about 1 minute.