Preheat the oven to 350 degrees F. Roll out the pie dough into a 12-inch round on a lightly floured surface. Ease into a 9-inch pie plate; fold the overhanging dough under itself and crimp as desired.
Whisk the eggs in a large bowl. Stir in the coconut oil, half-and-half, 1¼ cups shredded coconut, the sugar, flour, lime juice and all but ½ teaspoon lime zest. Pour into the prepared crust. Bake until the filling is set and the crust is golden brown, 50 to 55 minutes. (Tent the crust with foil if it is browning too quickly.) Transfer to a rack and let cool completely, 1 to 2 hours.
Meanwhile, spread the remaining 1 tablespoon shredded coconut on a baking sheet and bake until golden brown, 3 to 5 minutes. Beat the heavy cream and vanilla in a large bowl with a mixer on medium-high speed until soft peaks form, about 3 minutes. Spoon the whipped cream onto the pie. Sprinkle with the toasted coconut and reserved lime zest.