Preheat the oven to 350°F (180°C) and line a 12.25×8.125-inch (31×20.5 cm) baking tray with parchment paper.
With an electric mixer or a stand mixer, beat egg whites until soft peaks form. While the mixer is still on, slowly pour in the sugar and then the yolks. Grind spices and add to the batter. Finally add in the sifted flour.
Grease the parchment paper with melted butter, then pour the cake batter in an even single layer. Sprinkle with shredded coconut and bake for 10-12 minutes.
Remove from the oven, cover with a damp towel, then place in the refrigerator to cool.
For the mango curd:
Puree fresh mango in a food processor until smooth. Transfer to a small saucepan, pour in lime juice, and ½ cup sugar. Bring to a simmer over medium heat, stirring to dissolve the sugar.
Meanwhile, whisk egg yolks, egg, and remaining ¼ cup sugar in a medium bowl for about 2 minutes until pale and fluffy.
As you continuously whisk the eggs, gradually pour in the hot mango mixture, then transfer the result steadily back into the saucepan. Cook over medium heat, whisking constantly, until curd thickens, about 5–7 minutes (do not let it boil). Remove from heat and add butter a couple of pieces at a time, whisking until fully incorporated before adding more.
Strain curd through a fine-mesh sieve into a large measuring glass bowl or nonreactive bowl and cover, pressing plastic wrap directly onto surface. Chill for at least 2 hours until firm.
Prepare the spiced rum syrup with rum, sugar, and infuse the spices.
Remove cake roll from the fridge, remove the damp towel, then brush the cake with syrup.
Spread the mango curd all other the cake, leaving a border all around. Add in passion fruit, and just a few pieces of tropical fruit such as pineapple, kiwi, mango or other tropical fruits of your choice. Roll the cake on the shorter side, while leaving the joint on the bottom part. Transfer to a serving tray.
Melt white chocolate with heavy liquid cream in the microwave, stirring every 10 seconds, until completely melted. Pour all over the cake roll, then quickly sprinkle with shredded coconut. Decorate cake roll, then place in the fridge for at least 2 hours before serving.