Preheat the oven to 350°F (175°C) and lightly grease two 8-inch round pans. In one bowl, whisk together flour, baking soda, and salt.
In another, beat butter and sugar until light and fluffy. Add eggs one at a time, then mix in vanilla, sour cream, and mashed bananas until smooth.
Gradually stir in the dry ingredients just until combined. Fold in chopped walnuts and white chocolate chips.
Divide the batter evenly between the pans and bake for 30–35 minutes, until a toothpick inserted in the center comes out clean.
Cool for 10 minutes, then transfer to a wire rack. Once cooled, spread half the custard on one layer, add the second cake, and cover with the rest.
Garnish with banana slices and walnuts. Chill for 30 minutes before slicing or serve right away for a softer bite.