Make the filling: Bring the milk to a simmer in a medium saucepan over medium heat. Whisk the sugar, cornstarch, vanilla and egg in a medium heatproof bowl until smooth. Gradually whisk half of the hot milk into the sugar mixture, then return to the pan with the remaining milk. Reduce the heat to medium low and cook, whisking constantly, until the mixture boils and thickens, 2 to 3 minutes. Transfer to a bowl (strain through a fine-mesh sieve if it looks lumpy), then stir in the chocolate until melted. Press plastic wrap directly onto the surface and refrigerate until cold, at least 1 hour.

Meanwhile, make the ganache: Put the chocolate and salt in a large heatproof bowl. Bring 1 1/2 cups heavy cream to a simmer in a saucepan over medium heat; pour over the chocolate and let sit 5 minutes, then whisk until smooth. Pour 3/4 cup of the ganache into a liquid measuring cup and set aside at room temperature. Refrigerate the remaining ganache in the bowl until thick but not set, about 1 hour.

Assemble the cake: Put 1 cake layer on a platter; spread the filling on top, stopping about 1/2 inch from the edge. Top with the second cake layer and press down gently.

Add the remaining 2 tablespoons heavy cream to the chilled ganache and beat with a mixer on medium speed until just fluffy, about 1 minute (do not overbeat). Frost the whole cake with the whipped ganache. Pour the room-temperature ganache on top, letting it drip down the sides. Let set before slicing, about 30 minutes.

Photograph by Levi Brown