In a bowl, toss the eggplant with the salt. Transfer to to a colander or strainer and place over the bowl. Let drain for I hour.
Rinse the eggplant well and pat it dry with paper towels.
Line a rimmed baking sheet with several layers of paper towels. In a large, preferably nonstick pot or skillet over medium heat, warm 1/2 cup oil until hot but not smoking. Add the eggplant and sauté until nicely golden brown on all sides and sorta tender, about 10 minutes.
Using a slotted spoon, transfer the eggplant to the baking sheet lined with paper towels to drain.
Add the celery and the fennel to the pot or skillet and cook, stirring, for 1 minute. Add the zucchini and sauté for 3 minutes. Transfer the vegetables to the paper towels along with the eggplant.
Add the remaining oil to the pot or skillet and, still over medium heat, sauté the garlic and onion until golden, about 5 minutes.
Stir in the tomatoes, olives, capers, raisins, vinegar, and sugar and cook, stirring occasionally, for 10 minutes.
Return the reserved eggplant, celery, fennel, and zucchini to the tomato mixture and cook for 10 minutes, stirring or folding the vegetables occasionally and ever so gently so as not to break up the pieces and turn the mixture to mush. Season to taste with salt and pepper.
Carefully transfer the eggplant caponata to a wide, shallow dish and let it cool for 1 hour. Cover and refrigerate for at least 8 hours and up to several days.
About 1 hour before serving the eggplant caponata, remove it from the refrigerator, and bring it to room temperature. Sprinkle with the pine nuts, almonds, and basil just before serving.