To make the soup: Preheat an oven to 400 degrees F. In a baking dish, combine the tomatoes, shallots, garlic, and olive oil. Season with kosher salt and pepper and toss well to combine. Top with 3-4 sprigs of fresh thyme.
Roast for 45 minutes, until the tomatoes, shallot, and garlic are soft and the tomatoes have released their juices. Transfer the contents of the baking dish (all the juices too!) to a high-powered blender and blend until smooth. Add the broth if the soup is a little thick, 2-3 fresh basil leaves, and season to taste with salt and pepper. Blend until smooth.
Pour soup into bowls and drizzle with heavy cream or coconut cream. Top with more fresh basil.
To make the grilled cheese: heat a skillet over medium heat. Add two slices of each cheese to each sandwich and lightly spread the mayo on both sides of the sandwich.
Add the butter to the skillet and after it has melted and is foamy, add the sandwiches to the skillet. Cook for 2-3 minutes per side or until golden brown and the cheese is melted. Serve immediately.