Beat goat cheese and butter until smooth. Add flour and salt and blend just until dough comes together. Shape into a disc and chill for 2 hours before rolling.
On a lightly floured surface, roll out pastry to ¼ -inch thickness. Line a 9-inch removable-bottom tart pan with pastry and chill for 15 minutes.
Preheat oven to 350 °F. Line pastry shell with foil and weight with pie weights, dried beans or rice. Bake for 20 minutes, then remove weights and foil and bake another 10 minutes, until lightly browned. Allow to cool.
For filling, whisk cornstarch and whipping cream in a saucepot to combine. Whisk in corn syrup, sugar, brown sugar and egg yolks. Cook mixture over medium heat, stirring constantly, until it thickens and becomes glossy. Remove from heat and stir in butter, vanilla and salt. Stir in coconut and chill.
To assemble, preheat oven to broil. Place pineapple on baking sheet and sprinkle with brown sugar. Broil 2 minutes until sugar melts and arrange pineapple over chilled filling. Crumble goat cheese over and sprinkle with crushed pink peppercorn.