Preheat the oven to 350°F (175°C). Grease and flour a 9-inch round cake pan.
In a medium bowl, whisk together the all-purpose flour, baking soda, baking powder, and salt. Set aside.
In a large bowl, using an electric mixer, cream 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 vanilla extract.
Stir in the mashed bananas and sour cream until combined.
Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined. Do not overmix.
Fold in the chopped whole almonds gently with a spatula.
Pour the batter into the prepared cake pan and smooth the top with a spatula.
Sprinkle the sliced almonds evenly over the top of the batter.
Bake in the preheated oven for 45 to 50 minutes, or until a toothpick inserted into the center comes out clean.
Remove the cake from the oven and let it cool in the pan for 15 minutes.
Turn the cake out onto a wire rack and allow it to cool completely before serving.