Butter both sides of the bread, and place them on a baking sheet. Bake at 325 degrees for 4 minutes per side. Set aside.
2 tbsp butter, 6 slices thick sourdough bread
In a dutch oven, or other pot, heated over a medium pot melt the remaining tablespoon of butter. Stir in the onions and garlic. Cook, stirring occasionally, just until the onions are soft and translucent.
1/2 white onion, 1-2 tsp minced garlic
Stir in the bay leaf, nutmeg, and salt & pepper, to taste. Stir in the tomato paste and reduce the heat until the sauce is at a simmer. Simmer for 5 minutes, stirring occasionally.
1 bay leaf, pinch of nutmeg, salt and pepper, 2 tbsp tomato paste
Slowly add the cream & milk, whisking constantly until they're fully incorporated. Bring the mixture to a boil, then immediately remove the pot from heat.
1/4 cup heavy cream, 1/2 cup milk
To a large mixing bowl, add the eggs. Whisking, add 2 tbsp of sauce, to temper. Once completely incorporated, slowly slowly pour in the rest of the sauce, whisking constantly until the mixture's incorporated and combined completely.
3 eggs
Spray a 9x13 baking dish lightly with cooking spray. Add two bottom pieces of bread to it. Top them with the Swiss cheese. Place middle slices on top. Top those with the cheddar slices. Place top slices on top.
4 slices Swiss cheese, 4 slices sharp cheddar cheese
Slowly pour the tomato soup sauce evenly over top of the sandwiches. Sprinkle the shredded Parmesan evenly out over top of the soup covered sandwiches.
1/4 cup Parmesan cheese
Bake again at 325 degrees for 30 minutes, or until golden brown and the cheese is bubbly. Let the sandwiches rest 1-2 minutes, serve & enjoy!