Preheat your oven to 200°F. Line a baking sheet with parchment paper and set aside.
In the bowl of a stand mixer, whip the egg whites with the salt until they start to firm up. While mixing, add the sugar in a tablespoon at a time, giving the sugar time to dissolve within the egg whites. When the mixture is glossy and holding stiff peaks (a good test is to tilt the bowl – if they don't move, they're good to go), turn off the mixer and gently fold the cornstarch and lime juice in by hand.
Use a spatula to gently dump the meringue onto the parchment paper in a circle roughly the size of a dinner plate. Using the spatula, spread the merengue out from the center so that the edges are raised and there's a dip in the middle – this dip will help hold the cream and compote later on. Bake in the oven for an hour, then turn off the oven without opening the door and allow the merengue to cool for another hour.
While the meringue is cooling, make the compote. In a heavy bottomed saucepan, combine the berries, sugar, and lime juice. Cook over medium-high until the sugar is dissolved, then bring to a boil. Be careful, as the mixture will froth, and molten sugar is hot! Cook at a low boil until the mixture is thickened, about 15 minutes. Take off the heat and allow to cool completely.
When you're ready to assemble the pavlova, whip the cream and sugar together on high in a stand mixer until stiff peaks begin to form (about 5 minutes). Stir in the lime zest. Spoon the whipped cream into the merengue disk and top with blackberry compote and some more lime zest. Slice and serve, or just dig in with your fork and enjoy!