For the deviled ham, pulse-process ingredients in food processor into almost-smooth, very finely chopped spread.
Liberally brush 1 side of 8 slices of bread for 4 sandwiches with the melted butter.
Build sandwiches: bread with the butter side facing down, 2 slices Swiss cheese, some deviled ham, 2 slices cheddar cheese, and another slice of bread with the buttered side out.
Grill sandwiches over medium heat on nonstick griddle pan until cheese is melted and theyre deeply golden.