Prepare cake mix according to package directions in two 9-inch round pans. Cool completely.
For custard: Whisk milk, sugar, cornstarch, and egg yolks in saucepan. Cook over medium heat until thick. Remove from heat; stir in butter and vanilla. Cool completely.
Slice cooled cake layers horizontally. Spread custard between layers and on top (not sides).
For ganache: Heat cream until simmering. Pour over chocolate chips; let sit 5 minutes. Stir until smooth. Pour over cake center, allowing it to drip slightly.