Step 1

Cut 1 garlic clove in half and set aside. Smash remaining 5 garlic cloves and peel. Peel 2 onions and coarsely chop. Peel 2 carrots and coarsely chop. Open and drain 28-oz. can tomatoes into a colander set over a large bowl to catch juices.

Step 2

Heat 3 Tbsp. oil in a large pot or Dutch oven over medium. Add garlic, onion, and carrots; season with salt and pepper. Cook, stirring often, until onion is translucent and just starting to brown around the edges, 8–10 minutes.

Step 3

Add 1 tsp. paprika and stir to coat vegetables. Cook, stirring, until fragrant. Add whole tomatoes and cook, stirring often, until tomatoes start to burst and break down, 10–15 minutes.

Step 4

Meanwhile, grate 4 oz. cheddar cheese on the large holes of a box grater.

Step 5

Add 15-oz. can crushed tomatoes, reserved tomato juices, 2 Tbsp. Worcestershire sauce, and 1 cup water to pot and season with salt and pepper. Bring to a simmer, reduce heat to low, and cook 8–10 minutes, just to help flavors meld.

Step 6

Remove from heat and purée soup with an immersion blender until smooth.

Step 7

Stir about ¼ cup hot soup into ¼ cup sour cream in a small bowl, then stir back into soup (for a creamier soup, feel free to add more). Taste and season with more salt and pepper, if needed. Don’t let soup come back to a boil at this point or sour cream may split.

Step 8

Place a rack in top position of oven; heat broiler. Place 4 slices bread on foil-lined rimmed baking sheet and drizzle both sides with remaining 2 Tbsp. oil.

Step 9

Broil bread until one side is golden and toasted, then remove from oven and turn slices. Broil until second side is golden.

Step 10

Remove from oven and rub cut sides of remaining garlic cloves over top of toasted bread.

Step 11

Arrange grated cheese over bread, dividing evenly. Broil until cheese is melted and bubbling.

Step 12

Ladle soup into bowl and top with a dollop of sour cream.

Step 13

Cut bread into soldiers and serve with soup.

Step 14

Do Ahead: Soup can be made 3 days ahead. Let cool, cover, and chill. Reheat gently over medium-low, stirring occasionally.