For the pineapple tiramisu, prepare ready-made sponge cake base.
For the liqueur cream, soak the gelatine in cold water and boil a cup of whipped cream. Beat the yolks with salt and sugar until foamy. Then add the hot whipped cream. Allow to simmer briefly, then remove from heat. Mix liqueur, lime zest and juice. Squeeze out the gelatine and dissolve in the cream. Chill the cream, stirring occasionally. Whip remaining whipped cream until stiff and fold in.
Peel pineapple, remove core. Slice 3/4 of the pineapple, puree the rest, drain juice through a cloth and squeeze fruit puree firmly.Heat sugar until it caramelizes slightly, add pineapple juice and orange liqueur, cook until slightly thick. Spread sponge cake with caramel and the cream, alternate liqueur and pineapple over it.
Chill the pineapple tiramisu overnight and sprinkle with chopped pistachios before serving.