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Step 1
Make the custard: In a medium saucepan, whisk together egg yolks and sugar until well combined. Whisk in cornstarch and salt. In a slow, steady stream, whisk in milk and then the cream. Add butter. Cook mixture over medium-low heat, stirring constantly with a wooden spoon, just until it starts to thicken. Immediately whisk mixture until smooth, then continue to cook and stir custard until it has come to a very low boil for 2 minutes, about 6 to 8 minutes total. Strain custard through a fine mesh sieve into a small bowl, pushing it through with a small spatula. Stir in vanilla. Cover with plastic wrap, pressing the plastic directly onto the surface. Chill for at least 3 hours and up to 24 hours.
Step 2
Prepare the cake: Heat oven to 325 degrees. Butter a 9-by-2-inch round baking pan, generously greasing the sides, and line it with parchment paper. Butter parchment paper. In a medium bowl, whisk together flour, baking powder and salt.
Step 3
In a small saucepan, bring the milk and butter to a simmer over medium heat. When the butter is melted, remove pan from heat. In a large bowl, beat eggs and sugar with an electric mixer until pale and thick, about 4 to 6 minutes. With the mixer running on low, add the milk mixture and beat until combined. Then add flour mixture and vanilla and beat until combined.
Step 4
Transfer batter to the prepared pan and smooth the top. Bake until a toothpick inserted into the center comes out clean, 30 to 35 minutes.
Step 5
Transfer to a rack and let cool 10 minutes. With a very thin knife, cut around the edge to release the cake from the side of the pan. Carefully flip the cake onto the rack, then turn it right-side-up to cool completely.
Step 6
Assemble the cake: Using a serrated knife, carefully cut the cake into two layers and place the bottom layer on a serving plate. Stir custard, and spread it onto the cut side of the bottom half. Replace the top half of the cake, cut side down.
Step 7
Prepare the glaze: In a small saucepan over medium-low, heat the cream to a simmer. Remove the pot from the heat and pour cream over the chocolate chips, oil, salt and let stand for 3 minutes. Whisk until smooth. Spread the glaze evenly over the top of the cake.