Preheat oven to 350 degrees F. Grease a 9x13 pan and set aside.
In a medium bowl, whisk together the flour, baking soda, and salt. Set aside.
In a large bowl, cream together the butter and sugar until creamy and smooth, about 3 minutes. Beat in the eggs, one at a time, then stir in the Greek yogurt and vanilla extract. Mix in the mashed bananas.
Slowly add the dry ingredients and mix until flour disappears. Spread cake batter evenly into the prepared pan.
Bake for 25-35 minutes, or until a toothpick inserted into the center comes out clean. Allow cake to cool completely.
While the cake is cooling, make the peanut butter frosting. In the bowl of a stand mixer, beat the butter and peanut butter on high until smooth. Slowly add the powdered sugar, 1/4 cup at a time. Beat on high until powdered sugar is incorporated. Add the milk and vanilla extract. Beat until frosting is smooth and desired consistency.
Frost the banana cake with peanut butter frosting. Cut into squares and serve.
Note-store covered cake on the counter for 3-4 days. I think the cake gets better as it sits.