Butter each slice of bread on 1 side. Put 4 slices of bread, butter side down, into a large skillet. Top with a slice of cheese and 1/2 cup deviled ham. Place another slice of bread, butter-side up, onto each sandwich. Cover the skillet, put it on medium heat, and cook until the bottoms are nicely browned, about 5 minutes. Turn the sandwiches over and cook until the bottoms are browned, about 3 minutes. Serve while hot.
Combine all ingredients in a food processor and blend until smooth. Use as a sandwich filling or spread on crackers for a snack.