Peel the pineapple, quarter it lengthwise and cut out the hard stalk. Cut approx. 300 g flesh into small cubes. Peel and finely dice onions. Caramelize sugar and some water in a pot until golden brown.
Add the pineapple, onions and vinegar and boil the sugar loose. Simmer until the liquid has almost evaporated. Season with salt and pepper and stir in cranberries. Remove the chutney from the stove and let it cool down.
Cut cheese and ham into 8 pieces each. Peel, wash and roughly grate the potatoes. Stir in eggs. Season with salt and pepper. Heat 2-3 tablespoons of oil in a pan. Squeeze the potato mixture a little.
Form 4 Rösti from half of the potato mixture in the pan, adding 1 piece of ham and 1 piece of cheese each and frying over medium heat for 8-9 minutes, turning. Add 2 tablespoons of oil to the pan.
Bake 4 more Rösti from the remaining mixture. Arrange Rösti and chutney on plates, garnish with thyme.