Preheat the oven to 350°F (175°C). Grease and flour two 8-inch round cake pans.
In a medium bowl, whisk together the flour, baking soda, and salt. Set aside.
In a large bowl, beat the softened butter and granulated sugar together until light and fluffy, about 3 minutes.
Add the eggs one at a time, beating well after each addition.
Mix in the mashed bananas, Greek yogurt, and vanilla extract until combined.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Do not overmix.
Fold in the chopped walnuts if using.
Divide the batter evenly between the two prepared cake pans and smooth the tops.
Bake for 45 to 50 minutes, or until a toothpick inserted into the center comes out clean.
Remove from the oven and allow the cakes to cool in the pans for 10 minutes, then turn out onto wire racks to cool completely.
While the cakes cool, prepare the vanilla buttercream frosting: in a large bowl, beat the softened butter until creamy.
Gradually add the powdered sugar, one cup at a time, beating well after each addition.
Add the vanilla extract and 2 tablespoons of milk, and beat until smooth and fluffy. Add more milk if needed to reach spreading consistency.
Once the cakes are completely cool, place one cake layer on a serving plate and spread a layer of frosting over the top.
Place the second cake layer on top and frost the top and sides of the entire cake evenly.
Decorate as desired and refrigerate the cake for at least 30 minutes before serving to set the frosting.