Preheat the oven to 400 degrees. Spread the coconut flakes out on a baking sheet and toast for 5 minutes. Stir and toast an additional 3 minutes, or until golden brown. Allow to cool. Pulse in a food processor for a smoother custard or leave whole for a more pronounced coconut texture.
Meanwhile, place a sheet of parchment paper in the pie crust and fill with pie weights or dried beans. Bake the crust for 15 minutes, or until the edges are starting to brown. Remove from the oven, remove the pie weights and parchment, and prick the bottom all over with a fork. Return to the oven and bake an additional 6-7 minutes or until the bottom is starting to brown. Remove from the oven.
Optional step, but recommended: Whisk together the leftover egg white and 1 Tablespoon water. Brush all over the crust, sprinkle the edges with sugar, and return to the oven for about 2 minutes or until hard and shiny. This helps seal the crust and prevents a soggy bottom.
To make the coconut custard filling, beat together the eggs and yolk until smooth. Add the sugar, vanilla, salt, and nutmeg and beat again until well combined. Stir in the milk and coconut.
Place the blind baked pie crust on a baking sheet. If your pie edges are already browned, cover them with foil or a pie shield.
Carefully pour the filling into the crust. Transfer the pie to the oven. The pie will be quite full so take it slow and steady. Bake for 40-45 minutes, or until a knife inserted in the center comes out clean.