Step 1

Arrange a rack in the middle of the oven and heat the oven to 375°F. Line a rimmed baking sheet with parchment paper.

Step 2

Prepare the following, placing each on the baking sheet as you complete it: Trim and cut 2 pounds ripe tomatoes (skip cutting if using grape or cherry tomatoes) and 1 medium red bell pepper into rough 1-inch chunks. Thinly slice 1/2 medium yellow onion. Cut 1 head garlic in half crosswise, exposing the cloves.

Step 3

Drizzle with 1/4 cup olive oil. Sprinkle with 1 teaspoon of the kosher salt, 1/2 teaspoon black pepper, and 1/2 teaspoon granulated sugar. Toss together with your hands until evenly coated. Arrange into an even layer with the garlic cut-side down. Top with 2 fresh rosemary sprigs.

Step 4

Roast until the tomatoes are softened or the small tomatoes burst open, 55 minutes to 1 hour. Let cool slightly until cool enough to handle the garlic, about 5 minutes.

Step 5

Squeeze the garlic cloves out of the garlic head onto the baking sheet and discard the peels. Pick the leaves from the rosemary and place on the roasted vegetable mixture; discard the stems.

Step 6

Heat 2 tablespoons olive oil in a large, heavy-bottomed pot or Dutch oven over medium heat until shimmering. Add 3 tablespoons tomato paste and cook, stirring constantly, until it darkens slightly in color, about 2 minutes. Add the roasted tomato mixture, including any juices on the baking sheet. Cook until the tomato paste is fully mixed into the tomato mixture, 2 to 3 minutes.

Step 7

Add 2 cups low-sodium vegetable broth and season with the remaining 1/2 teaspoon kosher salt. Bring to a boil. Reduce the heat as needed and let simmer for 5 minutes to let the flavors meld.

Step 8

Turn off the heat. Blend directly in the pot with an immersion blender until smooth, or transfer in two batches to a stand blender and blend until smooth. If the soup is too thick, add more broth a little at a time as needed to thin it out.

Step 9

Taste and season with more kosher salt as needed. Serve topped with freshly cracked black pepper, a drizzle of olive oil, and a few torn fresh basil leaves if desired.