To make the pavlova, place a rack in the center of the oven and preheat it to 300 F. Line a baking sheet with parchment paper and draw a 9-inch circle in the middle (use a baking pan as a guide). Flip the paper over and set the baking sheet aside.
Combine the sugar, cornstarch, and ginger in a medium bowl and rub ginger into the sugar with your fingertips until the ginger is no longer in clumps and the sugar is scented with ginger.
Clean the bowl and whisk attachment of a stand mixer well. Dry them both well. Place egg whites in 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 the lime juice and continue to beat on high until glossy stiff 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 of the oven and immediately lower the oven temperature to 250 F. Bake until the outside is crisp, about 2 hours, 30 minutes. If the pavlova gets too brown or starts to crack you can turn the oven down to 200 F. Turn oven off and let the pavlova cool completely 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 to 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 coconut whipped 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 curries, smoothies, etc.) 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 thick and 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 toasted coconut, slice and serve.