Coarsely crumble the Oreo biscuits with a knife. Mix ricotta, vanilla sugar and sugar. Whip the cream until stiff. Gradually fold into the ricotta. Alternate with the Oreos in a large dessert bowl, beginning and ending with a layer of cream.
Cover and chill for about 3 hours.
Meanwhile, peel the pineapple, quarter it lengthwise and remove the hard stalk. Finely dice the flesh. Wash the limes hot and grate the skin finely. Halve the limes and squeeze the juice. Mix pineapple, lime peel, juice and brown sugar.
Add a little pineapple salsa to the tiramisu just before serving, otherwise the cream will become bitter. Add the rest of the pineapple salsa.