Preheat the oven to 400ºF and spread the tomatoes in a single layer in a large glass or ceramic baking dish. Drizzle with 1 tablespoon of the oil and sprinkle with salt and pepper. Bake 30 minutes, until tomatoes have caramelized.
In a large saucepan, heat the remaining 2 tablespoons of oil over medium heat. Add the garlic and sauté until fragrant, about 1 minute. Then add the zucchini and sauté 2 minutes.
Stir in the tomatoes and any accumulated juices from the baking dish. Add the chicken broth and bring to a simmer. Reduce the heat and simmer 10 minutes, until the zucchini is tender.
Add the basil leaves and let wilt. Then transfer to a large blender or food processor, or use an immersion blender, and blend until smooth. You may need to work in batches if using a blender.
Return to the pot and stir in the whipping cream and Parmesan until the cheese is melted. Taste and adjust seasonings as desired.
