For the pavlova, heat oven to 300°F and arrange rack in the center. Line a baking sheet with parchment paper and draw a 9-inch circle (using a cake pan as a guide) in the middle. Flip the paper over and set aside.
Combine the sugar, cornstarch, and ginger in a medium bowl and rub the ginger into the sugar until the ginger is no longer in clumps and the sugar is heavily scented.
Clean the bowl of a stand mixer and the whisk attachment well. Dry them thoroughly and place the egg whites into the bowl with the salt and whip on medium speed until soft peaks begin to form, about 5 minutes.
Gradually add the sugar mixture and then increase the speed to high. Whip on high speed for 2 minutes. Add lime juice and continue to beat on high until soft, glossy peaks form, 7 to 8 minutes more.
Using a rubber spatula, scrape the egg whites into a mound in the center of the parchment circle. Spread the mound to fill the traced circle then create a 3 1/2-inch wide and 1-inch deep well in the center.
Place on the center rack in the oven and immediately lower the oven temperature to 250°F. Bake until the outside is crisp, about 2 1/2 hours. If the pavlova gets too brown or starts to crack, you can turn the oven down to 200°F. Turn oven off and let pavlova completely cool in the oven, ideally overnight.
To make the tropical fruit salad, peel the zest off the lime using a vegetable peeler and place in a heatproof liquid measuring cup with the sugar. Add enough boiling water to reach the 1/3 cup line and stir until sugar is dissolved. Set aside to cool. Remove the lime zest from the syrup and gently toss with the fruit.
To make the whipped coconut cream, remove the cold cans of coconut milk from the refrigerator. Turn them upside down, open the cans, and pour out the liquid (reserve for another use like smoothies or curry), leaving the thick cream in the can. Scrape the cream into the bowl of an electric mixer, add the vanilla extract, and beat with the whisk attachment until fluffy, 4 to 5 minutes.
To assemble the dessert, place the pavlova on a serving dish, dollop the coconut cream on top and spoon the fruit over the cream. Sprinkle the top with the toasted coconut and serve.