Preheat the oven broiler on high.
Toss the tomatoes, garlic, and onion with oil on a foil lined baking sheet. Season well with salt and pepper. Broil until the tomatoes soften and the garlic and onion turn golden brown. Stir around the contents to allow them to get even coloring. Then remove from the oven and into a pot on medium heat.
Add the broth, cream, tomato paste, thyme, and sage. Bring to a simmer for about 5 minutes. Season with salt and pepper to taste. Stir to incorporate everything together. Remove from the heat. Remove the thyme sprigs.
Place in a blender. Blend until smooth.
Heat a nonstick pan on medium heat. Once hot, add the oil. Brown the ham slices on both sides then remove from the pan.
Layer the bread with cheese, ham, and cheese, and top with a bread slice. Spread the butter on both of the outer sides of the sandwich.
Lower the heat in the pan to medium low. Cook the sandwich to golden brown on both sides and until the cheese has melted completely, covered with a lid.
Add the lemon slices and mint to the sparkling water. Serve over ice if desired.
Cut in half and serve with soup, crackers, and lemon mint spritzer.