Spread the butter on one side of each piece of bread.
Place one slice of bread in the skillet, butter side down.
Assemble the first sandwich - 2 slices of cheese, 2 slices of ham, tarragon, scallions, 2 slices of cheese, and the second slice of bread and butter side up.
Cook over low heat for 3-5 minutes. Turn the sandwich over once the bread is golden brown and the cheese has started to melt.
Cook on the second side for an additional 3-5 minutes, until bread is golden brown, the cheese is melted, and the ham is heated.