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.
Roast the peppers and tomatoes in the oven for 25 minutes, until the skins are charred and the vegetables are soft.
Remove the peppers and tomatoes from the oven and let them cool slightly. Once cool enough to handle, peel the skins off the red peppers and discard the skins.
Heat the olive oil in a large pot over medium heat. Add the chopped onion and cook for 5-7 minutes, until translucent.
Add the minced garlic, smoked paprika, and dried thyme to the pot. Cook for another 1-2 minutes until fragrant.
Add the peeled roasted red peppers and roasted tomatoes to the pot, stirring to combine.
Pour in the vegetable broth, then add salt and black pepper. Bring the mixture to a boil, then reduce heat and simmer for 10 minutes.
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 blend until smooth.
Return the soup to low heat and stir in the balsamic vinegar and maple syrup. Adjust seasoning with additional salt and pepper if needed.
Ladle the soup into bowls and garnish with fresh basil leaves before serving.