Preheat oven to 425°F. Combine water, butter and sugar in a medium saucepan and bring to a boil; stir until butter melts. Add all flour at once and quickly stir with a wooden spoon until dough comes together. Continue stirring until a film coats bottom of saucepan and dough is glossy, about 2 minutes. Transfer mixture to bowl of a standing mixer and beat at medium-high speed for 1 minute. Add eggs, one at a time, and beat at medium speed until thoroughly incorporated.
Transfer warm dough to a pastry bag fitted with a plain or star tip with a 1/3- to 1/2-inch opening. Pipe 2 1/2- to 3-inchlong "fingers" of dough onto an ungreased baking sheet, spacing at least 2 inches apart. Bake for 20 minutes; reduce heat to 375°F and bake for 10 to 15 minutes more, until golden brown and crisp. Transfer to a rack and let cool.
Make frosting: Bring 1/4 cup heavy cream just to a boil in a small saucepan. Remove from heat, add chocolate and stir until smooth; stir in oil and set aside.
Cut top third off each pastry. Spoon Pastry Cream inside bottom portions. Dip tops into cooled, melted chocolate and invert onto éclair bases.
For Pastry Cream, In bowl of an electric mixer, stir together 3 Tbsp. sugar, 1 1/2 Tbsp. flour and 1 1/2 Tbsp. cornstarch. Add 3 egg yolks and beat at medium-high speed until thick, about 5 minutes. Scald 1 cup milk in a saucepan; drizzle into yolk mixture. Return mixture to saucepan and cook, stirring, until custard is thick and begins to boil. Cook for 1 minute more, and then remove from heat. Strain into a bowl, stir in 1/2 tsp. vanilla extract and let cool. Cover with waxed paper directly on surface and chill until cold. Just before serving, beat 1/2 cup heavy cream until stiff. Fold into custard. (Makes 2 1/4 cups)