Preheat oven to 350 degrees. In a large bowl, cream butter, sugar, and brown sugar for 4 minutes or until light and fluffy.
Add eggs one at a time, mixing after each addition. Stir in vanilla.
In a small bowl, mash bananas with fresh lemon juice. Add to the bowl and mix together. Stir in buttermilk.
Fold in flour, baking soda, baking powder, and salt. Pour into lightly greased 18 x 13 baking sheet. I prefer to use light-colored baking sheets. Pour batter into the pan and evenly spread. Bake for 20-22 minutes or until a toothpick comes out clean. Let cool.
Cream Cheese Frosting:
Cream butter and cream cheese together for 3-4 minutes or until light and fluffy. Add powdered sugar and vanilla and mix together. Add heavy cream or milk until desired consistency. Spread frosting all over the cake.
Brown Butter Frosting:
Place butter into a skillet and heat over medium-low. Melt butter in a skillet and watch it become a deep golden color -- about 5 minutes. Remove from heat and transfer to a heatproof bowl. Let cool in the refrigerator until solid.
Once butter is solidified, whip butter, softened cream cheese, powdered sugar, and vanilla until creamy -- about 4 minutes. Add heavy cream or milk until desired consistency.
Spread frosting over cake. Cut bars into squares and serve. May serve cold or at room temperature. These banana bars freeze very well.