Finely chop the ham and pineapple. Mix with cream cheese, salt, pepper, and dried Italian herbs.
Preheat oven to 220°C (428°F). Unroll the first sheet of puff pastry and spread half of the cream cheese and pineapple mixture over it. Roll up tightly and cut into roughly 20 slices. Arrange the slices on a baking sheet lined with baking paper and sprinkle with grated cheese if desired. Repeat with the second sheet of puff pastry and remaining mixture.