Preheat oven to 350 degrees. Butter a 13 by 9-inch baking dish then set aside.
In the bowl of an electric stand mixer fitted with the paddle attachment (or in a large bowl and using an electric hand mixer), cream together sugar and butter then mix in sour cream and eggs (occasionally scrape down bowl throughout mixing process).
Stir in mashed banana and vanilla extract. Add the flour, salt and baking soda then mix well.
Pour batter into prepared baking dish, spread into an even layer and bake in preheated oven until toothpick inserted into the center comes out clean, about 33 - 38 minutes. Cool completely on wire rack before frosting.
For the frosting:
In the bowl of an electric stand mixer fitted with the paddle attachment (or using a mixing bowl and hand mixer), mix together butter, powdered sugar and vanilla bean seeds.
Slowly add in heavy cream and mix until smooth and fluffy. Spread over cooled cake. Store cake in refrigerator in an airtight container. Let rest and room temperature a bit before serving.