Spread each bread slice with mustard-mayonnaise sauce. Sprinkle 4 slices with chives; top with ham, tomato and cheese. Cover with remaining bread slices, sauce side down. Spread 1 tablespoon of the butter on tops of sandwiches.
Melt remaining 2 tablespoons butter in 12-inch skillet over low heat. Add sandwiches, buttered side up; cover and cook 3 to 4 minutes or until toasted.
Turn sandwiches; cover and cook an additional 3 to 4 minutes or until toasted and cheese is melted.