Preheat the oven to 175°C (350°F). Grease and flour a 9-inch round cake pan.
In a medium bowl, whisk together the all-purpose flour, baking soda, baking powder, and salt. Set aside.
In a large bowl, beat the granulated sugar and eggs together until pale and fluffy, about 3 minutes.
Add the vegetable oil and vanilla extract to the sugar and egg mixture and mix until combined.
Stir in the mashed bananas until evenly distributed.
Gradually add the dry ingredients to the wet ingredients and gently fold until just combined. Avoid overmixing.
Pour the batter into the prepared cake pan and smooth the top with a spatula.
Bake for 35 to 40 minutes, or until a toothpick inserted into the center comes out clean.
Remove the cake from the oven and allow it to cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.
While the cake cools, prepare the cream cheese frosting: In a medium bowl, beat the softened cream cheese and unsalted butter together until smooth and creamy.
Add the powdered sugar and lemon juice, and beat until the frosting is light and fluffy.
Once the cake is completely cooled, spread the cream cheese frosting evenly over the top.
Serve the cake chilled or at room temperature.