Preheat oven to 350°F. Oil and flour the bottoms of two 9-inch round cake pans.
Cream butter and sugar together at medium high speed in large mixing bowl until fluffy. Add oil; beat in eggs and egg yolks, one at a time, and vanilla. Whisk flour, corn starch, salt and baking powder together in a small bowl. Reduce mixer speed to low. Add flour mixture to butter mixture in thirds, alternating with milk, until batter is smooth. Pour batter into prepared pans.
Bake 20 to 25 minutes, until wooden pick inserted in center comes out clean. Cool on wire rack for 15 minutes. Remove from pans and cool completely.
Whisk sugar, corn starch and salt together in a small saucepan. Slowly stir in milk, then egg yolks. Cook over medium heat, stirring constantly, until mixture boils; boil 1 minute. Remove from heat; stir in butter and vanilla. Pour pudding into shallow dish and cover surface with plastic wrap. Cool in refrigerator at least 2 hours or until no longer warm.
To assemble Boston Cream Pie: Place one cake layer on serving plate. Top with cooled Vanilla Filling, spreading evenly to edges of cake. Top with second cake layer.
Place chocolate, butter and vanilla in medium bowl. Bring cream and corn syrup to a boil in a small saucepan. Remove from heat; pour over chocolate, butter and vanilla. Cover; let stand several minutes or until mixture can be whisked smooth (chocolate has melted completely). Cool until mixture is slightly thickened. Pour glaze over assembled cake, spreading gently to allow glaze to run down sides. If desired, smooth glaze around sides of cake.
Chill Boston Cream Pie in refrigerator at least 1 hour to allow chocolate to set.