In a 2 cup (or larger) measuring cup, add water. Stir in cornstarch until dissolved. Mix in eggs and vanilla. Set aside.  In a 3-quart saucepan, over medium heat, heat milk until bubbles form around the edges. Stir in chocolate until melted. Add sweetened condensed milk and whisk until combined. Stir in egg mixture. While stirring constantly, bring to a boil. Once mixture is really thick, remove pan from heat. Whisk in butter. Once butter is combined, carefully pour into prepared pie crust.
Refrigerate Chocolate Silk Pie overnight or at least 8 hours.