Preheat the oven to 425°F (220°C).
Place the halved red bell peppers, quartered tomatoes, quartered onion, and garlic cloves on a large baking sheet.
Drizzle the vegetables with 2 tablespoons of olive oil and toss to coat evenly.
Roast the vegetables in the preheated oven for 25-30 minutes, turning halfway through, until the peppers and tomatoes are soft and slightly charred.
Remove the vegetables from the oven and let them cool slightly.
Once cooled, peel the skins off the roasted red peppers and discard the skins.
Transfer the roasted red peppers, tomatoes, onion, and garlic to a large pot.
Add 4 cups of vegetable broth, 1 teaspoon smoked paprika, 1/2 teaspoon dried thyme, 1/2 teaspoon dried oregano, 1/2 teaspoon salt, and 1/4 teaspoon black pepper to the pot.
Bring the mixture to a boil over medium-high heat, then reduce the heat and simmer for 10 minutes to allow the flavors to meld.
Using an immersion blender, blend the soup until smooth. Alternatively, carefully transfer the soup in batches to a blender and puree until smooth, then return to the pot.
Stir in 1 tablespoon of balsamic vinegar and adjust seasoning with additional salt and pepper if needed.
Ladle the soup into bowls and garnish with fresh basil leaves before serving.