Preheat the oven to 350°F. Grease and line two 8-inch round cake pans with parchment paper.
In a large bowl, beat the cake mix, milk, oil, eggs, and sour cream until smooth and thick, about two minutes. Fold in the white chocolate chips, divide the batter evenly between the pans, and smooth the tops. Bake for 25 to 30 minutes, until a toothpick inserted in the center comes out clean. Cool briefly in the pans, then turn out onto a wire rack to cool completely.
Beat the butter until smooth. Gradually mix in the powdered sugar, then add the vanilla and 4 tablespoons of cream. Beat until light and spreadable, adding more cream if needed.
Place one cake layer on a serving plate and spread with buttercream. Add the second layer and frost the top and sides. Chill for 15 to 20 minutes to set the frosting.
Place the white chocolate in a heat-safe bowl. Heat the cream until steaming, then pour it over the chocolate. Let sit for 2 to 3 minutes, then stir until smooth and glossy. Cool slightly until pourable, then spoon the ganache around the edges of the chilled cake, letting it drip naturally. Finish with shredded coconut and let set before slicing.