Beat cream cheese, butter, eggs, and vanilla until smooth and fluffy. With the mixer on low, add in the box of powdered sugar and beat until creamy and combined. Spread over the first layer.
Meanwhile, make a butter sauce by combining butter, sugar, and evaporated milk in a saucepan. Bring to a simmer over medium heat and cook for about 5 minutes, whisking regularly. Remove from heat and whisk in vanilla extract.
Pour butter sauce over butter cake (either warm or after the cake has cooled) and serve.