Preheat oven to 275°F and grease and line a 9" x 13" pan with parchment paper.
In a small bowl, mash the bananas with a fork and mix in the juice of one lemon. Set aside.
In a large mixing bowl, using an electric hand mixer, beat the butter, granulated sugar and brown sugar until light and fluffy.
Add the vanilla paste and one egg and beat until incorporated. Add the second egg and continue to beat until well combined. Add the sour cream and beat until smooth.
Sift the flour, baking soda and salt together and add to the wet ingredients. Mix until just combined. Using a spatula, fold in the mashed bananas.
Pour the batter into the baking dish and bake for 50-60 minutes. The top should be golden brown. (Moist crumbs should cling to a toothpick inserted into the center when it's done.)
Once baked, place a towel in the freezer and put the banana cake on top for 45 minutes. Remove and then let cool completely before frosting.
Notes
To Store: Keep leftovers covered in the fridge for up to 4 days.