Preheat oven to 400°. Line a large rimmed baking sheet with foil.
Place tomatoes on prepared baking sheet; drizzle with 2 tablespoons oil, and sprinkle with 1 teaspoon salt.
Bake until tomatoes are slightly charred, approximately 45 minutes.
In a large Dutch oven, heat butter and remaining 2 tablespoons oil over medium-high heat. Add onion; cook, stirring occasionally, until tender, approximately 5 minutes. Add garlic; cook until fragrant, approximately 1 minute. Stir in basil and flour; cook for 1 minute. Whisk in broth, paprika, pepper, and remaining 1½ teaspoons salt until smooth. Add tomatoes and any juices, using the back of a spoon to break up slightly.
Working in batches, transfer mixture to the container of a blender; blend until smooth. Return to Dutch oven; bring to a boil over medium-high heat. Reduce heat to medium-low; simmer for 20 to 30 minutes, stirring occasionally. Serve warm.
Garnish individual servings with sour cream and pepper, if desired.
Recipe by TeaTime Magazine at https://teatimemagazine.com/2-roasted-tomato-bisque-recipe/