Heat panini grill or George Foreman-style grill for 5 minutes. (Alternatively, lightly grease a nonstick pan with nonstick spray on medium heat and cover with a lid.)
Spread the dressing onto the bread. Top with cheese, sauerkraut, corned beef and another slice of cheese and remaining bread slice. Repeat for remaining sandwiches.
When the panini grill is hot (or the pan), add the sandwich. Close the lid; grill 5 to 6 minutes or until cheese is melted and the sandwich is crispy. (If cooking on the stovetop, cook for 3 to 4 minutes per side.) Cut in half and serve with pickles and chips.