Heat oven to 300 degrees. Spray 12-cup nonstick Bundt pan with baking spray with flour. Coat the pan well to prevent sticking.
In a large mixing bowl, beat butter, cream cheese, and sugar on medium-high speed until light and fluffy, about 4 minutes. Add vanilla, eggs, egg yolks, and whole milk. Mix for 1-2 minutes.
Stir in flour and salt and mix just until combined, avoid overmixing. Fold all ingredients together.
Pour into prepared bundt pan. Gently tap pan on the counter to release air bubbles. Bake for 1 hour 15 minutes -- 1 hour 25 minutes, or until the cake tester comes out clean.
Let cake cool in pan for 15 minutes. Invert cake onto rack and let cool completely. Cut into cubes.
In a medium bowl, toss berries with sugar. Set aside and let juices form.
To make Custard Filling:
In a large bowl, beat together pudding mix and whole milk. In another bowl, whip cream cheese, and sweetened condensed milk until smooth and creamy. Add heavy cream and beat until soft peaks for about 5 minutes. Fold in the pudding.