Bring large pot of salted water to a boil. Add radiatore and cook until al dente, 6 to 7 minutes. Drain and let cool briefly; do not rinse. Toss pasta with 1 tbsp of the olive oil. Spread out evenly on baking sheet to cool while preparing ratatouille.
Heat 2 tbsp of the olive oil in large non-stick skillet over medium heat. Add eggplant, season with salt and cook, stirring frequently, until soft and starting to brown, 10 to 12 minutes. Transfer to large plate.
In same skillet (no need to wipe it), heat 1 tbsp of the olive oil over medium-high heat. Add zucchini and cook, stirring frequently, until tender-crisp, 3 to 4 minutes. Transfer to plate with eggplant.
Heat the remaining 2 tbsp olive oil in same pan. Add onion, bell pepper and garlic and cook, stirring frequently, until softened, 4 to 5 minutes. Add tomatoes, tomato juice, capers, hot pepper flakes and thyme and cook, stirring occasionally, until tomatoes have broken down into sauce, 8 to 10 minutes. Add cooked eggplant and zucchini. Bring to a gentle boil, then reduce heat to low and simmer until eggplant is soft, about 5 minutes. Remove from heat. Taste and adjust seasoning as needed. Discard thyme sprig.
Add cooked pasta to ratatouille mixture and toss to evenly coat noodles. Transfer to serving bowl. (The salad can be served warm or at room temperature.) Before serving, sprinkle with basil, top with mozzarella and drizzle with some olive oil. Leftovers can be stored in airtight container in refrigerator for up to 2 days.