Make the Cake: Preheat oven to 375 degrees F. Lightly grease a 9x13-inch baking pan; set aside.
In a medium bowl, whisk together the flour, baking soda and salt; set aside.
Using an electric mixer, beat the sugar and oil together on medium speed until completely combined. Add both eggs and beat to combine, then add the mashed bananas and vanilla extract and beat until combined. Reduce the speed to low and add the flour mixture in three additions, alternating with the buttermilk, mixing until combined. Use a rubber spatula to give the batter one last mix, then pour into the prepared pan.
Bake for 30 to 35 minutes, or until the top is golden brown and a thin knife inserted into the center comes out clean. Set on a wire rack to cool completely.
Make the Cream Cheese Frosting: With an electric mixer, cream together the cream cheese, butter and salt on medium speed. Reduce the speed to medium-low and gradually add the powdered sugar until it has all been combined. Add the vanilla extract, increase the speed to medium-high and beat until light and fluffy.
Spread the frosting over the cooled cake, cut into squares and serve. Leftovers should be covered with plastic wrap or placed in an airtight container and kept at room temperature or in the refrigerator for up to 4 days.