Combine powdered sugar, orange juice, and orange zest in a medium bowl and stir until a glaze forms.
For the gingerbread cake:
Preheat oven to 350 degrees Fahrenheit. Cut a long piece of parchment paper slightly less wide than an 8x8-inch baking dish. Lay the parchment paper in the pan, letting the paper hang over two opposite sides to create handles. Spray the pan and parchment paper with nonstick cooking spray.
Combine the gluten-free flour, sugar, brown sugar, baking powder, baking soda, and spices in a large mixing bowl and whisk to combine.
Add pureed banana, melted butter, eggs, and molasses, then mix well with a spatula until the mixture is emulsified and smooth.
Transfer the batter to the prepared pan and use a spatula to spread it around evenly.
Bake in the preheated oven until a toothpick comes out clean and it's golden brown, about 26 minutes.
Once the cake is done, wait at least 10 minutes before using the handles to lift the cake out of the pan.
Place the cake on the cooling rack and drizzle the glaze all over the top of the cake.