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1
Preheat oven to 350F.
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2
Spread coconut in an even layer in a pie plate and toast in middle of oven, stirring occasionally, until golden, 10 to 12 minutes.
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3
(Leave oven on for baking crust.)
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4
Cool coconut to room temperature, about 10 minutes.
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5
Pulse together flour, coconut, butter, confectioners sugar, and salt in a food processor until dough just begins to form a ball.
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6
Press dough onto bottom and up side of tart pan with floured fingers, then freeze until firm, about 10 minutes.
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7
Bake in pan on a baking sheet in middle of oven until golden, about 25 minutes, then cool completely in pan on a rack.
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8
Puree chopped mango (2 1/2 cups) with sugar, lime juice, and a pinch of salt in a food processor until smooth, about 1 minute.
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9
Sprinkle gelatin over 1/4 cup puree in a heatproof bowl and let stand to soften 1 minute.
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10
Set bowl over a saucepan of simmering water and stir until gelatin is dissolved.
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11
Remove bowl from heat and stir in remaining puree.
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12
Beat cream in a large bowl with an electric mixer until it just holds stiff peaks, then fold in puree.
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13
Set bowl with filling in a larger bowl of ice and cold water and chill, stirring occasionally, until thickened, 1 to 1 1/2 hours.
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14
Remove side of tart pan and spoon filling into crust, smoothing top.
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15
Chill, loosely covered, until filling is set, at least 8 hours.
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16
Before serving, let stand at room temperature at least 15 minutes but no longer than 30, then scatter diced mango over top of tart, leaving a 2-inch border around edge.
