In a large pot, melt 1 tablespoon of butter over medium heat. Add the diced onion and minced garlic, sauté until they are soft and fragrant, about 5 minutes.

Stir in the canned diced tomatoes and vegetable or chicken broth. Bring to a simmer, allowing the flavors to meld together for about 10 minutes.

Remove the pot from heat and use an immersion blender to puree the soup until smooth. If you don't have one, carefully transfer to a blender in batches.

Add the heavy cream, dried basil, salt, and pepper to taste. Mix well and return to low heat to warm through.

While the soup simmers, heat a skillet over medium heat. Butter one side of each slice of bread.

Place a slice of cheese between two pieces of bread, butter side out. Repeat with the remaining slices.

In the heated skillet, add the sandwiches and cook until golden and crispy, about 3-4 minutes per side.

Once the sandwiches are golden, slice them in half and serve immediately alongside the warm tomato soup.