Preheat oven to 425 degrees Fahrenheit.

Place the tomatoes, onions, and garlic on a large rimmed baking sheet. Drizzle with olive oil and sprinkle with salt and pepper.

Roast at 450 degrees Fahrenheit for 15–20 minutes or until slightly charred. Remove from oven and transfer the mixture to a soup pot.

Add the stock and bring to a boil. Season with salt and pepper, then cook for four to five minutes. Remove from heat and purée the soup using an immersion blender.

To prepare the croutons, layer the American cheese between two slices of rye bread.

Heat a skillet over a medium-high flame. Melt the butter, add one sandwich to the pan, and fry on both sides until brown and the cheese is melted.

Transfer to a plate to cool slightly. Using a sharp, serrated knife, cut into one-inch cubes.

To serve, ladle the soup into a bowl and top with croutons and ribbons of basil. Serve immediately.