Preheat oven to 350°F and grease a 13x9 inch baking pan.
In a large bowl, cream together the softened butter, granulated sugar, and light brown sugar until light and fluffy. Add in the oil and mix again.
1/2 cup unsalted butter, 1/4 cup vegetable oil, 1 cup granulated sugar, 1/2 cup light brown sugar
Beat in the eggs, then add in the mashed bananas, vanilla extract, and sour cream.
2 large eggs, 3/4 cup sour cream, 1 teaspoon vanilla extract, 1 & 1/2 cup bananas mashed
In a separate bowl, whisk together the flour, baking soda, baking powder, cinnamon, and salt.
2 cups all-purpose flour, 1 teaspoon baking soda, 1 teaspoon baking powder, 1/2 teaspoon salt, 1/2 teaspoon cinnamon
Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Do not overmix.
Pour the batter into the prepared baking pan and bake for 45-50 minutes, or until a toothpick inserted into the center comes out clean.
Let the cake cool completely in the pan on a wire rack.