Preheat the oven to 425 degrees F. Set out a large rimmed baking sheet.
Cut the tomatoes in half. Cut the onion into large wedges (peels on to protect the underside). Then cut off the top of the head of garlic so that all the cloves are exposed.
Place the tomatoes, onions skin-side-down, and head of garlic on the baking sheet. Drizzle with olive oil and salt and pepper liberally.
Roast in the oven for 35 to 45 minutes, until the tomatoes are very soft and the onions are crispy around the edges.
Carefully remove the papery charred onion skins and garlic skins. Use tongs to move the roasted produce to the blender. Add the juices. Cover and puree until smooth. (NOTE: Hot items in the blender can pop the top off due to extra pressure. Place a dish towel over the blender lid to be safe.)
Set a 5 to 6 quart pot over medium heat. Add the tomato puree, vegetable broth, bay leaf, rosemary, and smoked paprika. Bring to a simmer and simmer uncovered for 20 minutes, stirring occasionally.
Use tongs to remove the rosemary and bay leaf. (If you don’t like the texture of cooked rosemary leaves, you can puree the soup base again.)
Stir in the heavy cream and chopped basil. Taste, then salt and pepper as needed. If the soup tastes too acidic, stir in 1 tablespoon sugar. Serve warm.
