Preheat the oven to 150°C. Arrange the tomatoes on a baking sheet cut-side down. Drizzle with olive oil and sprinkle with salt. Slow-roast until the tomatoes are soft and wrinkled, about 1 hour. Set aside to cool. (The tomatoes can be made and refrigerated up to 1 day ahead.)
Preheat a waffle iron to medium-high. Brush one side of each bread slice with melted butter. Lay the bread out on a clean work surface, dry-side up. Spread each slice of bread with some of the mayonnaise. Top 4 bread slices with 2 tomato halves, slightly smashing them into the bread. Top with 3 cheese slices each and the remaining bread slices.
Place two sandwiches at a time in the waffle iron and gently close the lid (don't press down). Cook until the cheese is melted and the sandwiches are golden-brown, 6 to 10 minutes. Repeat with the remaining sandwiches. Cut in half and serve.
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