How to Make It
Preheat oven to 400°F. Lightly spray 2 rimmed baking sheets with cooking spray; arrange tomatoes, eggplant, carrots, onion, and garlic cloves in a single layer on baking sheets. Drizzle olive oil evenly over vegetables; sprinkle with pepper and 1 1/2 teaspoons of the salt. Roast in preheated oven until tender and lightly browned, about 40 minutes, rotating baking sheets halfway through.
Scrape vegetables and cooking juices into a large Dutch oven. Stir in vegetable broth, half-and-half, and remaining 1 1/2 teaspoons salt. Bring to a boil over medium-high. Remove from heat. Puree soup with an immersion blender. Stir in vinegar.
For Garlic Croutons: Preheat oven to 400°F. Heat 1/4 cup olive oil and 4 garlic cloves in a small saucepan over medium-high. Cook, swirling the saucepan often, until garlic turns golden brown, 4 to 5 minutes. Remove from heat, mash garlic gently with a fork, and cool about 5 minutes. Pour oil through a fine wire-mesh strainer; discard solids. Cut 1 (10-oz.) French baguette into 1/2-inch cubes, and place in a medium bowl; drizzle with oil, and sprinkle with 2 Tbsp. chopped fresh flat-leaf parsley, 1/2 tsp. kosher salt, and 1/4 tsp. black pepper. Toss to coat. Place in a single layer on a rimmed baking sheet. Bake in preheated oven 7 to 9 minutes. Let them cool slightly, about 2 minutes.
Ladle about 2 cups soup into each of 6 bowls, top each with 1/4 cup Garlic Croutons, and 2 tablespoons feta. Sprinkle with basil.