Arrange oven racks in bottom ⅓ of oven. Preheat oven to 450°F. Line two rimmed baking sheets with parchment paper.
Spread eggplant in an even layer on one prepared baking sheet; lightly coat with cooking spray and season with ¾ tsp salt. Spread zucchini and peppers across second prepared pan; lightly coat with cooking spray and season with ¾ tsp salt. Roast until lightly browned, stirring and rotating pans halfway through, 35-40 minutes.
While vegetables roast, heat oil in a large soup pot over medium-low heat. Add onion and remaining ½ tsp salt; cook, stirring frequently, until extremely soft, 10 minutes. Add garlic, red pepper flakes, fennel seed and Italian seasoning; cook, stirring a few times, 1 minute.
Add tomatoes and broth to pot; stir and bring to a boil over high heat. Reduce heat to low; simmer, uncovered, 10-15 minutes.
Add roasted vegetables to pot; stir and cook for flavors to meld, 5 minutes. Stir in basil.