Preheat the oven to 400°F.

Slice the red bell pepper into strips or bite-sized pieces. On a large baking sheet, toss the 1 pound cherry tomatoes and the sliced red bell pepper with 2 tablespoons of the olive oil so they are evenly coated. Spread them in a single layer.

Roast the tomatoes and bell pepper for 20–30 minutes, flipping or stirring once halfway through, until the tomatoes have burst and the pepper is soft. Remove from the oven and set aside.

Meanwhile, heat the remaining 2 tablespoons olive oil in a large pot or Dutch oven over medium heat. Add the diced yellow onion and diced celery, then add 1/2 teaspoon kosher salt, 1/8 teaspoon coarse ground black pepper, 1 pinch red pepper flakes, 1 teaspoon paprika, and 1 teaspoon dried basil. Cook, stirring occasionally, for about 5–6 minutes, until the onion is translucent.

Add the 4 cloves minced garlic to the pot and cook, stirring, for about 30 seconds until fragrant.

Add the roasted cherry tomatoes and roasted red bell pepper to the pot, then pour in 4 cups vegetable or chicken broth, add the 14 ounces crushed tomatoes, and stir in 1 teaspoon white sugar. Bring the mixture to a gentle simmer, then reduce the heat to maintain a low simmer and cook uncovered for 30–40 minutes.

Use an immersion blender to blend the soup in the pot until completely smooth. (If using an immersion blender, keep the blade fully submerged while blending to avoid splattering.)

Stir in 1 cup heavy cream and warm the soup for 2–3 minutes more (do not boil). Ladle into bowls and, if desired, drizzle a little of the cream over each bowl before serving.