Preheat oven to 375F.
Line a baking sheet with parchment paper.
Place flour in a mixing bowl.
Using a pastry cutter or fork, cut in butter until mixture is crumbly and dough holds together when pressed.
Transfer dough to previously prepared baking sheet; press and shape dough in a 10-inch circle. Set aside.
Combine water and butter in a large saucepan; bring to a rolling boil, making certain that butter is melted.
Remove from heat and stir in vanilla.
Add flour and whisk until well blended.
Return to heat and stir vigorously until mixture is shiny and pulls away from sides of pan.
Remove from heat and let stand 5 minutes.
Transfer mixture to your mixer’s bowl.
Add eggs, one at a time, beating well before adding the next egg.
Continue beating until mixture is smooth, shiny and holds together.
Spread mixture over prepared pie crust.
Bake for 30 minutes, or until lightly browned.
Set on a wire rack and let cool completely.
In the meantime, prepare the glaze.
Combine powdered sugar, butter, milk and vanilla in a mixing bowl; beat until thoroughly combined.
Spread over cake.
Sprinkle with toasted coconut.