Preheat the oven to 350°F. Spray a 9x9-inch metal baking pan with nonstick spray and line it with parchment paper.
Whisk dry ingredients: Combine the gluten-free flour, baking soda, baking powder and salt into a separate bowl and whisk quickly to combine.
2 cups 1:1 gluten-free flour, 1 teaspoon baking powder, 1 teaspoon baking soda, 1/2 teaspoon salt
Mix the wet ingredients: Add the butter and sugar to a large mixing bowl or the bowl of a stand mixer. Beat on high for about 3 minutes, until light and fluffy. Add the eggs one at a time, beating well after each addition. Add the mashed banana and vanilla extract and beat on medium high until incorporated.
3/4 cup unsalted butter, 1 cup granulated sugar, 1/2 cup light brown sugar, 2 eggs, 1 cup mashed ripe bananas, 1 teaspoon vanilla extract
Combine the batter with buttermilk: Add half of the flour to the banana mixture and beat well to incorporate then add 1/4 cup of the buttermilk and do the same. Repeat the process with the rest of the flour then the rest of the buttermilk and beat on high until fluffy.
1/2 cup buttermilk
Bake: Spread the cake batter into the prepared baking pan and bake in the preheated oven for 45-55 minutes, or until toothpick comes out clean. Start checking the cake at 30 minutes and cover with foil if it's starting to look too brown. Remove it from the oven and cool completely on a wire rack.
Make the frosting: While the cake is cooling, cream together the butter and cream cheese on high speed for about 3 minutes. Slowly sift in the powdered sugar then add the vanilla and beat until it's smooth and fluffy.
1/2 cup (1 stick) unsalted butter, 8 ounces cream cheese, 3 1/2 cups powdered sugar, 2 teaspoons vanilla extract, 1/4 teaspoon salt
Scoop the frosting on top of the cake and spread evenly to the edges before serving.