Combine the sugar, cornstarch, and salt in a medium saucepan. Gradually stir in the milk until smooth. Bring to a boil over medium heat, stirring constantly, and boil for 1 minute, until thickened. Remove from heat and stir in the butter and vanilla. Once the butter has melted, stir in the unsweetened flaked coconut. Cool the mixture completely.
In a medium bowl, beat the heavy cream with an electric mixer until medium peaks form. Using a spatula, fold the whipped cream into the cooled pudding mixture. Spoon into a prepared tart crust.
Toast the remaining flaked coconut in a skillet over medium-low heat until golden brown, 5-10 minutes. Allow to cool. Top the coconut cream tart with the cooled toasted coconut and chill until served.