Two whirls collide on our mangoâ€“coconut cream tart: squiggles of barely sweet whipped cream and corkscrews of slightly tart mango. Underneath it all is a chewy coconut filling and a flaky pate brisee crust.
Make the pate brisee: Pulse flour, salt, and granulated sugar in a food processor until combined. Add butter; pulse until mixture resembles coarse meal, 8 to 10 seconds. Drizzle 1/4 cup ice water evenly over mixture. Pulse until mixture holds together when pressed between 2 fingers (dough should not be wet or sticky). If dough is too dry, add more ice water, 1 tablespoon at a time, and pulse. Shape dough into a disk, and wrap in plastic wrap. Refrigerate until firm, at least 1 hour and up to 1 day. Let stand at room temperature 5 minutes before rolling.
Preheat oven to 375 degrees. Roll out pate brisee into a 15-inch round (1/8 inch thick) on a lightly floured surface. Fit dough into a 12 1/2-inch fluted tart pan with a removable bottom, pressing dough well into pan's edge. Trim edge flush with top rim of pan. Prick bottom all over with a fork. Freeze until hard, about 20 minutes. Line with parchment, pressing parchment deep into corners of pan so it is flush with dough and leaving a 3-inch overhang. Fold overhang over dough edge so it is not exposed. Fill with pie weights or dried beans, and bake until edge of shell begins to turn golden, about 30 minutes, rotating halfway through. Remove weights and parchment. Reduce temperature to 325 degrees. Tent edge with foil, and bake until golden brown, 25 to 27 minutes more. Let cool slightly, about 20 minutes.
Make the filling: Mix together granulated and brown sugars, salt, and cornmeal. Whisk in eggs, yolk, and vanilla; then butter and coconut. Spread filling into tart shell. Bake until just set and lightly golden, 22 to 24 minutes. Let cool completely.
Make the topping: Peel mangoes, and cut in half, removing pits. Brush with lemon juice. Very thinly slice each half crosswise. Beat together cream and confectioners' sugar until medium peaks form. Spread one-third of cream mixture over top of filling. Fill a pastry bag fitted with a large open star tip (such as Ateco #829) with remaining cream mixture, and pipe randomly spaced swirls of cream. Twist 3 to 5 mango slices at a time into spirals, and nestle between cream swirls. Heat corn syrup and water until combined. Brush mango spirals with syrup. Refrigerate tart until chilled, about 20 minutes and up to 4 hours.