Make the Pastry Cream: Heat the half-and-half, 6 tablespoons of the sugar, and the salt in a medium heavy-bottomed saucepan over medium heat until simmering, stirring occasionally to dissolve the sugar.
Meanwhile, whisk the egg yolks in a medium bowl until thoroughly combined. Whisk in the remaining 2 tablespoons sugar and whisk until the sugar has begun to dissolve and the mixture is creamy, about 15 seconds. Whisk in the cornstarch until combined and the mixture is pale yellow and thick, about 20 seconds.
When the half-and-half mixture reaches a full simmer, gradually whisk the simmering half-and-half into the yolk mixture to temper. Return the mixture to the saucepan, scraping the bowl with a rubber spatula; return to a simmer over medium heat, whisking constantly, until a few bubbles burst on the surface and the mixture is thickened and glossy, about 30 seconds. Off the heat, whisk in the butter and vanilla. Strain the pastry cream through a fine-mesh sieve set over a medium bowl. Press plastic wrap directly on the surface to prevent a skin from forming and refrigerate until cold and set, at least 3 hours or up to 2 days.
Make the Cake: Preheat oven to 350 degrees F. Grease and flour two 9-inch round cake pans; set aside.
In a medium bowl, whisk together the flour, baking powder, baking soda, and salt; set aside.
Using an electric mixer, cream together butter and sugar until light and fluffy, about 3 to 5 minutes. Scrape down the sides of the bowl and beat in the eggs, one at a time, beating for 1 minute between each addition. Beat in vanilla extract.
Add the dry ingredients all at once and beat on low speed until just combined. Add the buttermilk and beat on low for 1 minute, then increase the speed to medium and beat for 3 additional minutes.
Divide the batter evenly between the prepared pans. Bake for 25 to 35 minutes, or until a skewer inserted into the center of the cake comes out with just a few moist crumbs attached. Remove from the oven and cool for 10 minutes in the pans, then turn out onto wire racks and cool completely before assembling.
Make the Ganache: While the cake cools, make the chocolate ganache. Place the chocolate in a 4-cup measuring cup; set aside. Place the cream in a small saucepan over medium heat and warm until it just comes to a boil. Pour the cream over the chopped chocolate and let sit for 2 minutes. Begin whisking the mixture in the center, gradually working your way outward until the ganache is completely smooth. Set aside to cool, whisking occasionally, until it has thickened slightly, yet still a pourable consistency.
Assemble the Cake: Place one of the cake layers on a serving platter, then spread the pastry cream evenly over top. Place the second cake layer on top and pour the chocolate ganache into the center of the cake layer. Using an offset spatula, gently spread the ganache into an even layer over the top of the cake. Refrigerate until ready to serve.
This cake can be prepared up to 1 day in advance and should be kept in the refrigerator.
Half and half is a common dairy product in the U.S. but can be replaced with 50% whole milk and 50% heavy cream.