Preheat the oven to 180°C (fan forced) and line a large baking sheet with baking paper. Place the tomatoes cut-side up on the baking sheet, drizzle with 2 tablespoons of the olive oil, and sprinkle with salt and pepper. Roast for 1 hour or until the edges just start to shrivel and the insides are still juicy.
Heat the remaining 2 tablespoons of olive oil in a large pot over medium heat. Add the onions, carrots, garlic, and ½ teaspoon salt and cook until soft, about 8-12 minutes depending on how long it takes your pot to get up to temperature (cast iron is slower). Stir in the tomatoes, vegetable broth, vinegar, and thyme leaves and simmer for 20 minutes.
Let cool slightly and pour the soup into a blender, working in batches if necessary. Blend until smooth. Add most of the basil and pulse until combined.
Garnish the soup with basil leaves and feta, then serve with crusty bread.