Thinly slice the carambola and divide them among 4 plates.
Finely chop the parsley. Mix the olive oil, lime juice and coconut or agave syrup into a smooth dressing. Stir in the parsley. Drizzle the dressing on the carambola.
Cut the apples in half and remove the cores. Cut the flesh into thin strips. Remove the chicory leaves and place 5 chicory leaves on each plate. Fill them with a slice of Coppa and place the apple on top.