Place the diced eggplant in a colander, sprinkle with salt, and let it sit for about 30 minutes to draw out excess moisture. Rinse and pat dry.
In a large pan, heat the olive oil over medium heat.
Add the onion and celery, and sauté until soft, about 5 minutes.
Stir in the red bell pepper and cook for another 5 minutes.
Add the dried eggplant and cook until softened, about 8-10 minutes.
Stir in the canned tomatoes, green olives, capers, red wine vinegar, and sugar (if using). Season with salt and pepper to taste.
Simmer for 15-20 minutes, stirring occasionally, until the mixture thickens.
Remove from heat and let the caponata cool to room temperature.
Serve garnished with fresh basil or parsley. Enjoy on a crusty bread or as is.