Prepare Lime Granita: Boil water and sugar until dissolved, cool, then stir in lime juice. Freeze in a baking dish, stirring every 45 minutes until frozen (about 3 hours).
Make Meringue: Beat egg whites until foamy, then gradually add sugars and cornstarch. Beat to stiff peaks, spread on a parchment-lined sheet, and bake at 200°F for 60-70 minutes until crisp.
Prepare Tart Crust: Cream butter and sugar, mix in egg yolk, then add flour and salt until dough forms. Press into a tart pan or chill as a disk for at least an hour.
Bake Tart Shell: Blind bake the shell with foil and weights at 350°F for 20-25 minutes, then remove weights and bake until golden on the bottom.
Cook Mango Curd: Heat mango, lime juice, sugar, salt, and yolks over a double boiler, stirring until thickened. Add butter, stir, and strain the curd.
Bake Tart: Pour the mango curd into the tart shell and bake at 325°F for 15-20 minutes until set. Cool, then refrigerate.
Assemble and Serve: Top the tart with meringue pieces, lime granita, and a sprinkle of cracked coriander before serving.