How to Make It
In a colander set in a large bowl, toss the eggplant with 1 tablespoon of salt. Let drain for 45 minutes, tossing occasionally. Spread the eggplant on a paper towel-lined baking sheet and blot dry.
Meanwhile, bring a medium pot of water to a boil and fill a medium bowl with ice water. Add the celery to the pot and blanch for 30 seconds, then drain and plunge immediately into the ice water. Let chill for 5 minutes, then drain and pat dry.
In a large saucepan, heat 3 tablespoons of the oil. Add the garlic and basil and cook over moderately high heat, stirring, until fragrant, about 1 minute. Add the crushed tomatoes and bring to a simmer. Reduce the heat, cover and simmer for 30 minutes, stirring occasionally. Uncover and cook until slightly reduced, about 10 minutes longer. Remove from the heat and season with salt.
In a large skillet, heat 1/4 cup of the oil. Add the eggplant and cook over moderately high heat, stirring occasionally, until golden and tender, about 12 minutes. Transfer to a bowl.
Wipe out the pan and heat the remaining 1/4 cup of oil in it. Add the onion and cook over moderately high heat, until translucent, scraping up any browned bits stuck to the bottom of the pan, about 2 minutes. Reduce the heat to low and cook, stirring occasionally, until soft and lightly caramelized, about 13 minutes. Add the tomato sauce, blanched celery, olives, capers, vinegar and sugar. Bring to a simmer and cook over moderately high heat for 5 minutes, stirring occasionally. Add the eggplant and cook, stirring, until the caponata is thick, about 5 minutes longer. Remove from the heat and let cool slightly. Serve warm or at room temperature.