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Preheat oven to 175 degrees. Line 4 baking sheets with parchment. Trace nine 3 1/2-inch circles onto each sheet. Turn parchment marked-sides down.
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Heat sugar, egg whites, and salt in a heatproof bowl set over (not in) a pan of simmering water, whisking constantly, until warm to the touch and sugar is dissolved, about 3 minutes. Remove bowl from heat. Whisk on medium-high speed until peaks are stiff and glossy, about 4 minutes. Beat in food coloring.
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Dab meringue under corners of parchment to hold in place. Spread 3 heaping tablespoons meringue within edges of each traced circle. Sprinkle 1 teaspoon coconut each over 12 of rounds.
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Bake until meringues are dry but not taking on any color and can be easily pulled off parchment, 1 1/2 to 2 hours. Let cool completely on sheets on wire racks.
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Form 1/4-cup scoops of sorbet into 3-inch disks, using your hands or a small offset spatula. Place a sorbet disk on a plain meringue. Top with a second plain meringue and a second sorbet round, then end with a coconut-sprinkled round. Transfer to a parchment-lined baking sheet and freeze, at least 5 hours and up to 1 day. Repeat with remaining meringues and sorbet.
Cook’s Notes
The baking time for the meringues will vary depending on the humidity. Be sure to bake them until they pull off the sheets easily.
