Preheat the oven to 350 degrees F (175 degrees C). Grease and flour two 8-inch round pans.
In a small bowl, whisk together flour, baking soda, and salt; set aside.
In a large bowl, cream together white sugar, brown sugar, and butter until light and fluffy. Beat in eggs, one at a time. Mix in mashed bananas.
Add flour mixture alternately with buttermilk, mixing well after each addition. Stir in chopped walnuts.
Pour batter into the prepared pans.
Bake in the preheated oven until cake springs back when gently pressed, about 30 minutes.
Remove cake layers from the oven and place them on a damp tea towel to cool.
Once cooled, assemble and frost the cake as desired.
Notes
This banana cake is moist and flavorful, with the addition of chopped walnuts for extra texture. Allow the cake layers to cool completely before assembling.