Lightly spray a large baking sheet with nonstick spray then line with tomato halves, cut side up. Drizzle tomatoes with extra virgin olive oil then season generously with salt and pepper.
Wrap garlic cloves in foil with an extra drizzle of olive oil then place alongside tomatoes.
Roast for 1 hour, or until tomatoes are golden brown and very tender. Cool slightly.
Unwrap garlic cloves then transfer with tomatoes and their juices into a food processor or blender and pulse until tomatoes reach desired consistency.
Pour mixture into a large soup pot then add dried thyme, red pepper flakes, and broth then bring to a boil.
Reduce heat and simmer for 20 minutes. Taste and adjust seasonings if necessary.
Butter one side of each bread slice, then place cheese slices on the non-buttered side.
Top with remaining bread slices, buttered side out, then cook in a skillet over medium heat until both sides are very crisp and cheese is melted.
Remove from heat and let rest for 2 minutes. Cut sandwiches into cubes then divide among bowls of soup.