Defrost puff pastry slices side by side on the work surface. Peel the pineapple and cut it into 6 slices about 1 cm thick. Cut off brown firm coconut skin and grate the flesh coarsely
Heat butter in a coated pan. Add sugar and allow to caramelize. Add pineapple slices and simmer for 3-4 minutes on a low heat, turning
Place one pineapple slice in each of the greased tartlet cups (10 cm Ø each). Leave to cool and sprinkle with half of the grated coconut
Place puff pastry slices on top of each other and roll out 2-3 mm thin on a floured work surface. Cut out 6 dough circles (each approx. 12 cm Ø). Place circles on the pineapple slices and press the edges inwards
Bake the tartlets in a preheated oven (electric cooker: 200 °C/ convection oven: 175 °C/ gas: see manufacturer) for approx. 20 minutes until golden brown. Turn out of the tins and let cool on a cake rack. Wash the lime with hot water and tear thin strips from the lime using a pestle ripper. Serve Tartelettes hot or cold. Sprinkle with remaining grated coconut and lime zests