Mix the capers, green onions, and cream cheese until smooth. Spread some of the mixture on one side of each bread slice. Heat skillet over medium heat. Top four of the bread slices with a slice of cheddar, 2 ounces of lox, and some pickle slices. Top with the remaining bread slices (cream cheese side down).
Melt 2 tablespoons butter in a skillet. Add two sandwiches (or as many as will fit) and cook for 3 minutes; flip carefully and grill until bread is browned and cheese melts. Repeat with remaining butter and sandwiches.
Courtesy Wisconsin Milk Marketing board