In a large bowl, mix the corn syrup, eggs, egg yolks, brown sugar, butter, cinnamon, salt, and vanilla. Stir in the pecans and the coconut. Pour the filling into the pie crust.
Place the pie on a baking dish and transfer to the center rack of the oven. Bake for 60 to 70 minutes, until the center reaches 200ºF. The center should bounce back when tapped. Let the pie cool for at least 2 hours before serving.