Shake the can of coconut milk well; open the can and pour the contents into a 4-cup measure. Add half-and-half (about 1 1/8 cup) to the measured coconut milk to make 3 cups liquid.

In a large, heavy, nonreactive saucepan, whisk together the sugar and cornstarch until no lumps are visible. Add whole eggs and egg yolks, and whisk until smooth. Slowly add the combined milks while whisking, then add 1 teaspoon vanilla extract. Place over medium heat and stir constantly until mixture thickens—about 12-15 minutes. Remove from the heat and whisk in the butter until completely melted, then add 1 cup shredded coconut. Let the mixture cool slightly, then pour into the pre-baked pie shell and smooth the top. Butter a piece of parchment or plastic wrap then place it on top of the custard, and refrigerate for 4 hours (longer is fine).

Meanwhile, preheat the oven to 300°F. Spread about 1/4 cup shredded coconut (more, if you like) on a parchment-lined baking sheet. Place in the oven and toast for 10-12 minutes, tossing every few minutes. When golden brown, transfer to a small plate and set aside.

When the pie has finished chilling, beat the cream and confectioners sugar until stiff peaks form. Swirl the whipped cream on top of the pie, then sprinkle with the toasted coconut.