Heat the oven to 425°F. Rinse the tomatoes thoroughly, remove their stems, and slice them in half.
Remove the papery outer skin from the onion, trim away the ends, and cut the onion into quarters.
Slice the top from the garlic bulb so the cloves are exposed, keeping the base intact so the head remains together.
Coat the bottom of a 9-by-13-inch baking dish with the extra-virgin olive oil.
Arrange the halved tomatoes, quartered onion, and whole garlic bulb in the prepared dish. Season evenly with the paprika, dried oregano, salt, and black pepper.
If desired, gently toss the tomatoes and onion in the dish so the vegetables are thoroughly coated with the oil and seasonings.
Transfer the baking dish to the preheated oven and roast for 15–20 minutes, or until the tomatoes begin to burst and the onion develops a well-browned exterior.
Carefully remove the baking dish from the oven.
Place the Boursin cheese into the baking dish with the roasted vegetables, then add 1/4 cup water.
Return the dish to the oven and continue baking for another 15 minutes, until the cheese has melted and is lightly golden.
Transfer the roasted tomatoes, onion, melted cheese, and all accumulated juices and sauce from the baking dish to a blender or suitable mixing bowl.
Remove the roasted garlic bulb and gently squeeze the softened cloves from their skins into the other ingredients. Discard the garlic skin and remaining base.
Blend the mixture in a standard blender, or process it with an immersion blender, for approximately 1 minute. Continue until the tomatoes, onion, and garlic are fully puréed and the soup reaches the preferred consistency.
Pour the finished tomato soup into serving bowls. Finish each portion with a drizzle of heavy cream and a scattering of finely chopped fresh basil for added richness, color, and fresh herbal flavor.