Step 1

Fit a fine-mesh strainer over a medium bowl. Cut 2 tablespoons unsalted butter into small cubes.

Step 2

Place 4 large egg yolks, 1/2 cup granulated sugar, 3 tablespoons cornstarch, and 1/4 teaspoon kosher salt in a medium saucepan. Whisk until no dry bits remain and the mixture is well combined. Add 1 3/4 cups whole milk and whisk to combine.

Step 3

Cook over medium heat, whisking constantly, until the mixture begins to thicken, about 8 minutes. Once it thickens, continue to whisk, pausing every few seconds to check for bubbles. As soon as it begins to bubble, continue to whisk constantly for 1 minute. Remove the saucepan from the heat.

Step 4

Add the butter and 2 teaspoons vanilla extract or 1 teaspoon vanilla bean paste. Whisk until the butter is melted. Scrape into the strainer and push through the strainer with a flexible spatula. Scrape the pastry cream on the underside of the strainer into the bowl. Discard the contents of the strainer. Press a sheet of plastic wrap directly onto the surface of the pastry cream to prevent a skin from forming. Refrigerate until cold, at least 3 hours and up to 3 days.

Step 5

Place 3 large eggs in the bowl of a stand mixer (or large bowl if using an electric hand mixer). Let sit until room temperature.

Step 6

Meanwhile, arrange a rack in the middle of the oven and heat the oven to 325ºF. Coat the sides and bottoms of 2 (9-inch) round cake pans with butter. Line the bottom of each pan with a parchment paper round. Sprinkle a little all-purpose flour over the sides and bottoms, and tilt and shake to distribute evenly, tapping out the excess.

Step 7

Place 1 1/4 cups all-purpose flour and 2 teaspoons baking powder in a medium bowl and whisk to combine. Cut 6 tablespoons unsalted butter into small cubes and place in a microwave-safe measuring cup. Add 3/4 cup whole milk and microwave in 30-second intervals, stirring in between each, until the butter is melted, 60 to 90 seconds total. (Alternatively, heat the butter and milk in a small saucepan over medium heat.)

Step 8

Add 2 teaspoons vanilla extract and 1/2 teaspoon kosher salt, and stir to combine.

Step 9

Add 1 1/4 cups granulated sugar to the bowl of eggs. Beat with the whisk attachment on high speed until thick and doubled in volume, about 6 minutes. The mixture should fall back on itself in a ribbon and be pale yellow in color. Reduce the mixer speed to low and pour in the milk mixture in a steady stream. Add the flour mixture, a few spoonfuls at a time, and beat, scraping down the sides of the bowl halfway through, until just combined, about 30 seconds total.

Step 10

Evenly divide the batter between the pans (about 14 ounces or 2 3/4 cups each). Bake until the cakes are a light golden brown and until a tester inserted in the center of each cake comes out clean, 22 to 25 minutes.

Step 11

Place the pans on a wire rack and let cool for 15 minutes. Run a small offset spatula or thin knife around the edges of each cake to loosen. Flip the cakes out of the pans onto the rack and remove the parchment paper. Gently flip right side up, and let cool completely, about 30 minutes.

Step 12

Place one cake right-side up on a large flat serving plate or cake stand. Stir the pastry cream to loosen. Dollop onto the cake and spread into an even layer, going all the way to the edges. Place the second cake layer on top with the bottom facing up. Press down gently to adhere. Refrigerate for at least 2 hours or overnight.

Step 13

Coarsely chop 4 ounces bittersweet chocolate (or use 2/3 cup bittersweet chocolate chips) and place in a medium bowl. Add 1 tablespoon corn syrup and 1/8 teaspoon kosher salt.

Step 14

Place 1/2 cup plus 1 tablespoon heavy cream in a small microwave-safe bowl (or measuring cup) and microwave in 30-second intervals until it begins to bubble, about 90 seconds total. (Alternatively, heat in a small saucepan over medium-high heat until bubbling around the edges.)

Step 15

Immediately pour the cream over the chocolate. Let sit for 1 minute. Whisk until the chocolate is melted and the mixture is smooth. Pour the ganache over the chilled cake, letting it run down the sides of the cake. Refrigerate until the ganache is set, about 30 minutes.