Heat the oven to 220 C / 425 F and line a sheet pan 33 x 46 cm / 13 x 18 inch with parchment.
Arrange the peppers cut side down, tomatoes cut side up, and onion quarters and garlic cloves around them. Drizzle with 3 tbsp olive oil and sprinkle with salt, black pepper, and smoked paprika.
Roast for 35 to 40 minutes until the pepper skins are blistered and blackened in spots, the tomatoes have collapsed, and the onion edges are charred.
Let the pan cool for 10 minutes. Peel the charred skins off the peppers and discard. Squeeze the softened garlic cloves out of their skins.
Transfer the peppers, tomatoes, onion, and garlic to a blender with 1 cup / 240 ml of the broth. Blend in batches, venting the lid and holding a towel over the top, until smooth.
Pour the blended soup into a 5-quart / 4.7 L Dutch oven and stir in the remaining broth. Bring to a simmer over medium heat.
Simmer uncovered for 10 minutes, stirring occasionally, until slightly thickened.
Stir in the heavy cream and balsamic vinegar. Taste and adjust salt as needed.
Ladle into bowls and top with torn basil, a drizzle of olive oil, and red pepper flakes if using.