Preheat oven to 400 degrees F. Line a rimmed baking sheet with parchment paper.
Arrange tomatoes, peppers cut-side down, onion, and garlic on the prepared baking sheet. Drizzle with olive oil and season with salt and pepper.
Roast 40 to 45 minutes until vegetables are soft and lightly charred. Peel away pepper skins if desired.
Transfer roasted vegetables to a large saucepan. Add broth, basil or thyme, and smoked paprika. Simmer over medium heat 10 minutes.
Remove from heat and blend until completely smooth using an immersion blender or carefully in batches in a countertop blender.
Return to low heat. Slowly stir in sour cream until fully incorporated. Do not boil after adding sour cream or it may break.
If the soup tastes sharp or acidic, stir in sugar starting with 1/4 teaspoon. Adjust seasoning and serve hot, garnished with fresh basil if desired.