In a small mixing bowl add the crab meat, 3 tbsps of mayonnaise, onion, celery, chives & Old Bay Seasoning. Gently combine.
Evenly spread remaining mayonnaise on one side of each slice of bread. Heat a large skillet or griddle over medium-low heat. Add butter & allow to melt.
Divide half the cheese evenly on top of the bread slices. Spread the crab salad over the bread followed by remaining cheese. Top each with a second slice of bread, mayo side up. Transfer sandwiches to the pan.
When the underside is golden brown (~3 min) flip the sandwich & continue to cook. Gently press down on sandwich to brown & continue to cook until cheese has melted & underside is golden brown (~3 min).
Remove the melts to plates and cut in half. Serve hot.