Preheat your oven to 325°F (163°C) and grease three 8-inch round cake pans. Line the bottoms with parchment paper.
Melt the 5 oz white chocolate in a microwave-safe bowl in 30-second bursts, stirring until smooth. Set aside to cool.
In a large bowl, beat softened cream cheese and butter until creamy and free of lumps.
Gradually add sugar and beat until ultra-light and fluffy (about 3 minutes).
Add eggs one at a time, beating well between each addition.
Pour in the melted white chocolate and vanilla extract, and mix until combined.
In a separate bowl, whisk together cake flour, baking powder, baking soda, and salt.
Alternate adding dry ingredients and milk to the wet mixture, starting and ending with the dry. Mix just until combined—do not overmix!
Fold in the vegetable oil gently for the silkiest texture.
Divide the batter evenly among the prepared pans.
Bake for 28–32 minutes, or until a toothpick inserted comes out with moist crumbs.
Remove cakes from the oven and let them cool in the pans for 10 minutes, then turn out onto a wire rack to cool completely.
Warm heavy cream in a microwave or saucepan until just before boiling.
Pour over the white chocolate chips, let sit for 2 minutes, then stir until smooth.
Cool at room temperature until thickened but still pourable.
Melt 8 oz white chocolate and let cool.
Beat softened butter until pale and fluffy.
Add the melted chocolate, then gradually beat in the powdered sugar, vanilla, salt, and milk/cream as needed for a smooth, pipeable consistency.
Place the first cake layer on a serving platter. Brush with ganache, then spread a thick layer of buttercream.
Repeat with remaining layers, finishing with a layer of buttercream on top and around the sides.
Use a large star tip to pipe decorative swirls. Top with truffles and any other favorite decorations.