Spoon coconut into a small frying pan over medium heat. Cook, shaking pan 2-3 minutes until toasted. Transfer to a bowl. Add sesame seeds to the pan, cook, shaking pan 2 minutes until lightly toasted. Add the chilli, cook further 30 seconds. Add to the coconut. Set aside to cool.
Combine the dressing ingredients in a jug, season and whisk until well combined. Pour half into a large bowl. Using a mandolin, thinly slice the fennel and radish. Add to the dressing just before you are ready to serve. Toss gently to coat.
Cut the cheeks from the mangoes. Using a large spoon remove the mango fruit from the cheeks and slice. Add to the fennel with the cucumbers, prawns and parsley. Toss gently to combine.
Pile salad onto serving plates. Sprinkle with coconut chilli mixture. Spoon over the remaining dressing. Season and serve.