Preheat broiler to high and place a rack 1 rung below top. Halve eggplant lengthwise and pour a few tablespoons EVOO in a bowl. Brush the cut-side of eggplant with EVOO and season liberally with salt and pepper, place cut-side down in a rimmed baking sheet and roast 20-25 minutes to tender.
Meanwhile, heat a soup pot over medium to medium-high heat with EVOO, a couple turns of the pot to cover bottom, add onion and garlic and season with salt, and stir a few minutes until onions are translucent. Add chili paste and sundried tomato paste to pan and stir 1 minute, then add wine and stir a minute more, add tomatoes, passata, stock and sugar and bring soup to a bubble, reduce heat and simmer 20 minutes.
Scrape the flesh of the roasted eggplant away from the skins and add to the soup.
Puree soup with immersion blender and stir in torn basil leaves. Adjust salt.