Preheat the oven broiler to 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 place into a pot on medium heat.
Add the broth, cream, tomato paste, thyme, and sage. Bring to a low simmer for about 15 minutes. Season with salt and pepper to taste.
In the meantime: Add the oil and onions to a saucepan on medium heat; cover with a lid. Let the onions cook, stirring occasionally until they become soft and golden brown (if the onions get too dark add a tablespoon or two of water; this will smooth out the coloring). Remove from the pan and set aside. Use the pan to cook the burgers.
Mix together the ground beef, steak seasoning, and Worcestershire sauce and form oblong patties to fit the shape of the bread.
In a skillet on medium heat, cook the burgers on both sides to your desired doneness (see below) using a thermometer. Then remove and set aside.
Layer the bread with cheese, onion, and burger.
Grease the skillet with nonstick spray and place over medium-low heat. Cook the sandwich on both sides until the bread is golden brown and the cheese is melted.
In a bowl mix together the ketchup and mayo.
Finish the soup: Stir to incorporate everything together. Remove from the heat. Remove the thyme sprigs. Place in a blender. Blend until smooth.
Mix together the sparkling water and lemon. Serve over ice if desired.
Cut the sandwich in half and serve it with soup, pickles, and spritzer. Enjoy with sauce on the side.