Combine the cubed eggplant with a sprinkle of salt, placing it in a colander set over a bowl. Allow it to rest for approximately 30 minutes, then rinse thoroughly and pat dry to remove excess moisture.
In a large skillet over medium heat, warm 2 tablespoons of olive oil. Add the celery and cook, stirring frequently, for about 3 to 4 minutes, or until it begins to soften. Stir in the onion and garlic, cooking until the onion becomes tender and lightly golden, around 4 to 5 minutes. Using a slotted spoon, transfer the mixture to a separate bowl.
In the same skillet, heat the remaining 2 tablespoons of olive oil. Add the prepared eggplant and cook, stirring constantly, until it is lightly browned, about 5 minutes.
Incorporate the celery mixture back into the skillet, along with the tomatoes, olives, capers, tomato paste, and oregano. Bring the mixture to a gentle boil, then reduce the heat to low and simmer uncovered for approximately 15 minutes, or until the caponata thickens.
Season the caponata with red wine vinegar, sugar, salt, and black pepper to achieve a balanced taste. Transfer to a serving bowl, garnishing with fresh parsley.