Heat 2 tablespoons olive oil in a large wide pot over medium-high heat. Add the onion, eggplant, a big pinch of salt and a few grinds of pepper. Cook, stirring occasionally, until the vegetables are lightly browned and starting to soften, about 6 minutes. Stir in 1 more tablespoon olive oil, the garlic, chili powder and cumin and cook, stirring, until the spices are toasted, about 1 minute. Stir in 2 cups water, the tomatoes, beans, 3/4 teaspoon salt and a few grinds of pepper. Cover and bring to a boil, then uncover and reduce the heat to a simmer; cook until slightly thickened, about 15 minutes.
Meanwhile, grate the tofu on the large holes of a box grater onto a clean kitchen towel (not terry cloth). Gather up the sides of the towel and wring the tofu dry. Heat the remaining 2 tablespoons olive oil in a large nonstick skillet over medium-high heat. Add the tofu, spreading it out; cook, stirring once or twice, until well browned and crisp, 4 to 5 minutes. Season with salt and pepper.
Stir the tofu and corn into the chili and heat through, 5 minutes. Season with salt and pepper. Thin the chili with water, if needed.
Divide the chili among bowls. Top with avocado, cheese, cilantro and corn chips.