Preheat the oven to 300 degrees and position racks in the middle and lower thirds. Line 2 large baking sheets with parchment paper.

In a food processor, pulse the coconut, 1/3 cup of the sugar, and the cornstarch until finely ground. In the bowl of a standing electric mixer fitted with the whisk, beat the egg whites and salt at medium-high speed until firm peaks form. Add the remaining 2/3 cup of the sugar, 1 tablespoon at a time, and beat until stiff. Fold in the coconut mixture.

Transfer the meringue to a pastry bag fitted with a 1/2-inch star tip. Pipe 1 1/2-inch mounds of meringue onto the baking sheets, about 1 inch apart. Sprinkle with the pistachios and bake for 25 minutes, until the meringues are very slightly browned and set but not dry; shift the sheets from top to bottom and front to back halfway through for even baking. Turn the oven off, prop the door open about 8 inches and let the meringues dry for 1 hour. Transfer the baking sheets to racks and let the cookies cool completely.