Heat neutral oil to about 350°F and fry the cubed eggplant until golden on all sides. Transfer to a paper towel–lined tray and set aside.
In a large pan, heat olive oil and sauté the sliced onion and celery until soft and translucent, about 10–12 minutes.
Add the chopped tomatoes and cook for 3–4 minutes until they begin to break down.
Stir in the olives, capers, and toasted pignoli. Lower the heat and cook gently for 15–20 minutes.
In a small bowl, combine tomato paste, sugar, and red wine vinegar.
Add this mixture to the pan and cook for 3–4 minutes, allowing the vinegar to cook off and the flavors to deepen.
Add the fried eggplant and toss gently to combine.
Remove from heat and finish with fresh basil.
Let cool to room temperature or refrigerate before serving.
Drizzle with extra virgin olive oil before serving.