Preheat your oven to 350°F and line a 13x9-inch baking pan with parchment paper.
In a large bowl, mash the banana with a fork until very smooth. Whisk in olive oil and eggs. Add milk, vinegar and vanilla and whisk until blended.
Add oat flour or ground oats, almond flour and ground flax seed and whisk it in until evenly combined. Don't worry about over-mixing at this point. Let batter stand for 5-10 minutes to allow the oat flour to hydrate.
In a medium bowl, whisk together flour, baking powder, baking soda, ground cinnamon, nutmeg and salt until evenly blended.
Add the flour mixture and fold it in gently until mostly combined but a few streaks remain. Fold in berries if you choose to use them. Do not over-mix.
Scrape the batter out into the prepared baking pan and spread it out in an even layer. Bake for 12-15 minutes until lightly golden around the edges and firm to the touch. Transfer pan to a wire rack and let cool completely.
Once cool, slice the cake into 6 even squares 4 ¼ inches by 4 ¼ inches.
Make the frosting. Place very soft cream cheese in a small mixing bowl and blend well using an electric hand mixer until smooth. Add 1 tablespoon of cream and mix until it is smooth again. Add another tablespoon of cream and repeat. Gradually pour in remaining cream while mixing until it is incorporated and then whip until it forms soft peaks. Do not over-whip or it can turn grainy.
Immediately use the frosting to spread between the cake layers and then cover it with a thin layer. Place in the fridge for 30 minutes to firm up.
Stir up about ⅓ cup of runny peanut butter and spoon it gently over the edge, allowing it to drip down.
