How to Make It
Peel the eggplant and cut into 1-inch pieces. Heat a large heavy-bottomed saucepan with half of the extra virgin olive oil; add half of the eggplant and season with 1/4 teaspoon of kosher salt. Fry the eggplant cubes in two batches until golden brown, adding the second addition of olive oil and salt with the second batch. Remove from the oil and set aside.
Using the same pan, add the celery, red onion, garlic, and capers and season with salt and pepper. Cook over medium to low heat until vegetables have softened and look glossy, about 10 minutes. Add the diced tomatoes and sugar to the pan and stir to combine. Fold in the cooked eggplant and cook over medium heat for about 20 minutes, stirring every 4 minutes. Add the vinegar to the mixture and season with salt and pepper to taste.
Cook the pasta in a large pot of boiling salted water, stirring once or twice until al dente, about 7-8 minutes. Drain and reserve 1/2 cup of pasta cooking liquid.
Heat the caponata in a large skillet over medium heat and add the pasta water to the pan. Bring to a gentle simmer and toss in the pasta, stir until incorporated and heated through. Season with salt and pepper, and garnish with basil; drizzle lightly with olive oil. Serve warm or at room temperature.