Heat a contact grill (like George Foreman or panini grill) on high.
Lightly brush one side of each slice of bread with olive oil. Spread ranch dressing evenly over the other side of each bread slice. Place 4 slices of bread on work surface, oil side down. Layer ingredients on top of bread, beginning and ending with cheese. Top with remaining sliced bread, oil side up.
Place sandwiches, 1 or 2 at a time, on grill; close lid. Cook for 5 to 6 minutes, or until ham is hot and cheese is melted. Repeat with remaining sandwiches.