Bring a small pot of water to a boil. Place raisins in a small heatproof bowl.
Pour enough boiling water over raisins to cover. Set aside.
In a large pot over medium-high heat, heat oil until shimmering. Working in batches, arrange eggplant in a single layer and cook, stirring until golden, about 5 minutes. Using a slotted spoon, transfer eggplant to a plate; season with salt.
Into same pot, pour more oil if needed and heat over medium-high heat. Cook green and red peppers, stirring, until softened, about 7 minutes; season with salt. Using slotted spoon, transfer peppers to plate with eggplant.
In same pot over medium-low heat, combine onion and celery and cover with a lid. Cook, removing lid and stirring occasionally, until celery is soft, about 15 minutes.
In a medium bowl, whisk vinegar, capers, brown sugar, crushed red pepper flakes, and 1 tsp. salt.
Add garlic to pot and cook, stirring, until fragrant, about 1 minute. Add tomatoes, increase heat to medium, and simmer 10 minutes more.
Return eggplant and peppers to pot. Add vinegar mixture, raisins, olives, parsley, and pine nuts and stir to combine. Simmer, uncovered and stirring occasionally, until liquid is slightly reduced, about 10 minutes. Let cool.
