Thinly slice the tomatoes and lay them on a paper towel. Sprinkle with salt and let sit to release any water, about 15 minutes. Pat dry.
Lay out 4 slices of the bread on a work surface. Layer each with 2 slices of cheese, making sure that they cover to the edges. Follow with 2 slices of tomato and then 1 more slice of cheese. Close the sandwiches with the remaining bread. Thinly and evenly spread the butter on both sides of the bread using about 1 1/2 tablespoons of the butter for each sandwich.
Place 2 sandwiches into a nonstick medium skillet over medium heat. Cover the skillet with a lid and cook until the bread is evenly golden brown, about 2 minutes. Flip, cover again and cook until the bread is golden brown and the cheese is visibly melted, about 2 minutes more. Repeat with the remaining sandwiches.
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