For the Crust

1. Adjust the oven rack to the middle position and preheat the oven to 350°F.
2. Pulse the cookie crumbs, coconut, and melted butter in a food processor until coconut is finely ground. Press the crumbs firmly and evenly into the bottom and up the sides of a 9-inch deep-dish pie pan (the crust should be about ¼-in thick). Bake until golden, about 15 minutes, then set aside to cool. If the crust shrinks or cracks a bit, simply press it back together and up the sides while it's still hot.

For the Filling

1. In a medium bowl, whisk together the eggs, egg yolks, sugar, flour, cornstarch and salt. Set aside.
2. In a medium saucepan, combine the rum, cream of coconut, coconut milk and whole milk. Bring to a boil; then turn off the heat. Whisking constantly, slowly ladle about a cup of the hot milk mixture into the egg mixture; whisk well to combine. Whisking constantly, gradually add the remaining milk mixture to the egg mixture in 3 or 4 additions; whisk well to combine. Return the mixture to the sauce pan. Cook over medium-high heat, whisking constantly, until the mixture reaches a boil and thickens, about 2 minutes. The filling must boil for at least 30 seconds in order to fully thicken. Off the heat, whisk in the butter until fully incorporated.
3. Pour the hot filling into the cooled pie shell and smooth the surface with a spatula; press plastic wrap directly against the surface of the filling and refrigerate until firm, at least 6 hours and up to 12 hours. (Any longer than 12 hours and the crust will start to soften.)

For the Topping & To Serve

1. Up to 3 hours before serving, whip the cream in the bowl of an electric mixer fitted with the whisk attachment. When it starts to thicken, add the sugar and rum. Continue to whip until it forms soft peaks. Top the pie with the whipped cream and sprinkle with cooled toasted coconut chips.
2. Slice the pie into wedges, wiping your knife clean between slices, and serve cold.
3. Note: Unsweetened coconut flakes can usually be found at Whole Foods or organic markets. If you can't find them, feel free to substitute ½ cup sweetened flaked coconut (the stuff in the blue bag available everywhere). Simply toast it in a 350°F oven, stirring often so it browns evenly, until lightly golden.
4. Note: For an even prettier presentation, this pie can be made in a 10-inch tart pan with a removable bottom. Note that the crust won't be quite as thick.