Step 1: Sauté Aromatics : In a large pot, heat olive oil or butter over medium heat. Add chopped onions and sauté for 4–5 minutes, until soft and translucent. Stir in minced garlic and cook for 30 seconds, until fragrant.
Step 2: Add Tomatoes and Broth : Add canned tomatoes (with juice), tomato paste, and broth. Stir well, breaking down the tomatoes with a spoon. Season with salt, pepper, Italian seasoning, and sugar (if needed). Bring to a gentle boil, then reduce heat and simmer for 15–20 minutes, allowing flavors to develop.
Step 3: Blend the Soup : Remove from heat and let cool slightly. Use an immersion blender directly in the pot, or carefully transfer soup to a blender. Blend until smooth and creamy. (Leave it slightly chunky if you prefer rustic texture.)
Step 4: Add Cream and Basil : Return soup to the pot over low heat. Stir in heavy cream and chopped basil. Simmer for 5 more minutes, stirring occasionally. Add a tablespoon of butter for an extra silky finish (optional).
Step 5: Prepare Grilled Cheese Sandwiches : Spread softened butter on one side of each bread slice. Place 4 slices, buttered side down, on a skillet or pan over medium heat. Add shredded cheese evenly on top (and any extras like tomato slices or caramelized onions). Cover with remaining bread slices, buttered side up. Grill until golden brown and cheese is melted — about 3–4 minutes per side. Remove and slice diagonally for classic presentation.