Preheat the oven to 350°F. Grease and flour a 9 x 9-inch baking pan. Set aside. Scatter walnuts out onto a baking sheet in a single layer. Bake 5 minutes. Remove the pan and allow the nuts to cool while you prepare the cake batter.
In the bowl of a stand mixer fitted with the paddle attachment (or a large bowl using a hand mixer), cream butter and both white sugar and brown sugar. Add mashed bananas, water, eggs, and vanilla extract. Mix on medium-low 1 minute.
Add the gluten-free flour, baking powder, baking soda, and a pinch of fine sea salt. Mix on medium-low speed JUST UNTIL the flour is combined. Over-mixing will result in an overly dense and chewy crumb. NOTE: if using additional add-ins (chocolate chips, butterscotch chips, or dried banana chips), fold them in now using a rubber spatula.
Scrape the batter into the prepared pan and bake for 40 minutes. Test for doneness by inserting a toothpick into the center of the cake. The cake is done when there is no visible batter on the toothpick, only moist crumbs or it's clean.
Remove cake from oven. Allow it to stand in the pan for 5 to 8-minutes. Invert the cake onto a wire rack and then again so the top of the cake is right side up. Allow to cool completely before frosting, about 1 hour. ProTip: If taking along to a gathering, place the cake on a platter or back into the pan. Cutting this cake before applying the maple walnut cream cheese frosting makes portioning and serving super easy. Again, consider this if it's serving as a take-along to a party or cookout.