Pour the tomato soup into a pan and place it on the griddle or side burner. Stir in milk, basil, oregano, black pepper, and salt to taste. Heat gently, stirring occasionally, until warmed through.
If using mayonnaise, spread it on one side of each slice of sourdough bread. Melt butter directly on the griddle.
Place four slices of bread on the griddle butter side down with the mayonnaise side facing up if using. Layer each slice with two pieces of smoked cheddar, an even layer of smoked salmon, and two slices of smoked Gouda. Top with the remaining bread slices, mayonnaise side out.
Cook until the bottom slices are golden brown, then carefully flip each sandwich.
Continue cooking until the second side is browned and the cheese is fully melted.
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