Step 1

Heat oil and butter in a large saucepan over medium-high. When butter melts, add onion, garlic, and 2 teaspoons salt. Cook, stirring often, until soft and golden, 6 to 8 minutes. Stir in flour; cook 1 minute. Add tomatoes and juice, broth, and basil sprigs. Bring to a boil, then cover, reduce heat to low, and simmer until tomatoes are very soft and breaking down, about 20 minutes. Discard basil sprigs and let cool slightly.

Step 2

Working in batches, puree soup in a blender until smooth; return to saucepan. Season to taste with salt and pepper. To serve, rewarm over medium-low heat, divide among bowls, and top with basil leaves, a drizzle of oil, and more black pepper.