Preheat the oven to 425 degrees F. Set out a large rimmed baking sheet.

Prepare the vegetables: Cut the 3 pounds plum or Roma tomatoes in half. Cut the 1 large sweet onion into large wedges, keeping the peels on. Cut off the top of the 1 head garlic (10–14 cloves) to expose the cloves.

Arrange the halved tomatoes, onion wedges (skin-side-down), and the head of garlic on the prepared baking sheet.

Drizzle generously with 3 tablespoons olive oil, then season liberally with salt and pepper (to taste).

Roast in the preheated oven for 35-45 minutes, until the tomatoes are very soft and the onions are crispy around the edges.

Remove the baking sheet from the oven. Carefully remove the papery charred onion skins and garlic skins from the roasted vegetables.

Transfer the roasted tomatoes, onion, and garlic, along with any accumulated juices from the baking sheet, into a blender.

Puree the mixture until it is smooth. (For safety, place a dish towel over the blender lid when blending hot contents).

Pour the pureed tomato mixture into a 5-6 quart pot set over medium heat.

Stir in the 32-ounce vegetable broth, 1 bay leaf, 2 fresh rosemary sprigs (or 1 teaspoon dried rosemary), and 1 teaspoon smoked paprika.

Bring the soup to a simmer, then reduce heat and continue to simmer uncovered for 20 minutes, stirring occasionally.

Remove the rosemary sprigs and bay leaf from the soup using tongs.

Stir in ½ cup heavy cream and ¼ cup fresh chopped basil leaves.

Taste the soup and adjust seasoning with salt and pepper (to taste) as needed. If the soup tastes too acidic, stir in 1 tablespoon granulated sugar.

Serve warm.