To prepare filling, cook pudding according to package directions. Chill for 1 hour. To prepare pastry, in a heavy saucepan, heat butter, water and salt over medium-high heat until mixture boils and butter melts. Reduce heat to low. Vigorously stir in flour all at once until mixture forms a ball. Transfer pastry to a bowl; cool for 5 minutes. Stir in eggs, 1 at a time, beating well after each addition. Preheat oven to 400 F.
Grease a baking sheet. Drop dough into 12 mounds, about 5 inches apart, on prepared baking sheet. Spread each mound into a 4x½-inch rectangle, piling dough on top and slightly rounding sides. Bake until golden, 35 minutes. Remove from oven ; make a 1-inch-long slit on side of each éclair. Reduce oven temperature to 375 F. Bake for 10 minutes. Transfer to a wire rack to cool. To prepare frosting, heat butter and chocolate over low heat, stirring until melted. Remove from heat. Stir in sugar, milk, and vanilla until smooth. Slice éclairs in half. Spoon about 1 Tbsp of filling onto each bottom half and replace tops. Spread tops with frosting.