Preheat the oven to 425°F (220°C).
Place the halved red bell peppers and quartered tomatoes on a baking sheet lined with parchment paper, cut side down.
Drizzle 1 tablespoon of olive oil over the peppers and tomatoes.
Roast in the preheated oven for 25 minutes, until the skins are charred and the vegetables are soft.
Remove the baking sheet from the oven and allow the peppers and tomatoes to cool slightly.
Once cooled, peel the skins off the roasted red peppers and tomatoes and discard the skins.
Heat the remaining 1 tablespoon of olive oil in a large pot over medium heat.
Add the chopped onion and sauté for 5-7 minutes until translucent.
Add the minced garlic and cook for another 1 minute until fragrant.
Add the peeled roasted red peppers, peeled roasted tomatoes, tomato paste, smoked paprika, dried thyme, salt, and black pepper to the pot.
Pour in the vegetable broth and stir to combine all ingredients.
Bring the mixture to a boil, then reduce heat and simmer for 15 minutes to allow flavors to meld.
Remove the pot from heat and use an immersion blender to puree the soup until smooth. Alternatively, carefully transfer the soup in batches to a blender and puree until smooth.
Stir in the 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.