How to Make It
For Pastry Cream:
Whisk together sugar and cornstarch in a medium saucepan. In separate bowl, whisk together milk and egg yolks until combined. Add milk mixture to saucepan with 2 Tbsp. butter. Place saucepan over medium-high and whisk constantly until mixture begins to boil. Continue whisking for 30 seconds until mixture is thick. Remove from heat, and stir in 1 Tbsp. butter and vanilla. Transfer mixture to refrigerator.
For Pastry Decorations:
Preheat oven to 400°F. Prepare 1 piping bag with plain 1/2-inch piping tip. Combine butter, sugar, salt, and water in a saucepan over medium-high. Bring to boil, add flour, and stir vigorously until dough comes together and a dry film coats the bottom of the pan, about 2 minutes. Remove from heat and set aside for 3 minutes. Add one egg, and stir vigorously until fully incorporated. Add another egg and stir again until smooth, shiny, and thick. Place in piping bag, and pipe 1 1/4-inch-diameter rounds on a parchment paper-lined baking sheet. Using a damp finger, press down any peaks of dough so the surface of each round is perfectly domed. Bake for 10 minutes, lower oven temperature to 350°F and bake until golden brown, 15-18 minutes. Cool completely before cutting each puff in half horizontally, removing tops and dusting with powdered sugar. Set aside. Place bottoms in a food processor, and pulse until pastry becomes fine crumbs. Transfer to a baking sheet, and bake at 400°F until toasted and brown, about 5 minutes. Set aside for later use.
For Cake Layers:
Preheat oven to 350°F. Grease three 9-inch round cake pans. In a medium-sized bowl, whisk together flour, baking powder, and salt. Set aside. In a stand mixer, cream together butter, shortening, and sugar until light in color, about 3 minutes. Add eggs one at a time, waiting until each egg is fully incorporated before adding the next. Beat on medium-high for 3 minutes. In a separate bowl, combine buttermilk, oil, and vanilla. With mixer on low, slowly stream buttermilk mixture into butter mixture. Increase to medium speed and beat until light and fluffy, about 5 minutes. Add flour mixture and mix until combined, about 1 minute. Pour into prepared cake pans, and bake until lightly golden and a toothpick inserted into the center comes out clean, about 30 minutes. Cool in pans for 10 minutes before removing to a wire rack to cool completely.
For Eclair Buttercream:
Cream together butter and powdered sugar until lightened in color, about 3 minutes. Add vanilla and salt. Then add 6 Tbsp. prepared Pastry Cream and the toasted pastry crumbs from Step 2. Beat until combined. Place buttercream into piping bags.
Place 3 oz. chopped chocolate and 4 Tbsp. unsalted butter in a medium saucepan. Place over medium heat and stir until just melted. Remove from heat. Use a serrated knife to remove any domes from the Cake Layers so they are even and flat. Pipe a ring of Eclair Buttercream around the edge of the surface of the first Cake Layer, creating a border. Pour half of the melted chocolate inside the ring of buttercream, spreading across the top of the Cake Layer. Remove pastry cream from the refrigerator, mix with a fork until smooth, and spread half of the pastry cream on top of the chocolate. Place second Cake Layer on top of the first, and repeat process of piping buttercream border and spreading remaining chocolate ganache and pastry cream. Top with final Cake Layer, putting it face down so the smooth bottom of the layer forms the top surface of the cake. Pipe remaining buttercream on top and sides of cake. Smooth with a spatula. Refrigerator until firm, about 1 hour. Heat remaining 3 oz. chopped chocolate with remaining 4 Tbsp. butter in a medium saucepan over medium heat. Stir until melted, then set aside until just above room temperature (about 90°F). Pour over top of chilled cake and use a spatula to gently push chocolate across the surface, allowing chocolate to drip over the edges of the cake. Place Pastry Decorations reserved from Step 2 around the perimeter of the top of the cake. Let chocolate set before serving, 15 minutes.