For the cake: Preheat the oven to 350 degrees F. Line a 9-by-13-inch baking pan with parchment, leaving about 4 inches of overhang on the long sides. Generously grease the parchment with the butter.
In a stand mixer on low speed, beat the cake mix, water, oil, eggs and mashed bananas for 30 seconds. Raise the speed to medium and beat for another 2 minutes, scraping down the bowl as necessary.
Pour the batter into the prepared baking pan. Bake until a toothpick inserted into the center comes out clean, 30 to 35 minutes. Let cool.
Using the parchment "handles," remove the cake to platter. With a fork, poke holes every 1/2 inch in the top of the cake.
In a large bowl, whisk together the condensed milk, coconut cream and whipping cream and then pour evenly over the top of the cake. Cover and refrigerate until the mixture is absorbed into the cake, at least 2 hours and up to 4 hours.
For the frosting: In a stand mixer fitted with the whisk attachment, whip the cream to soft peaks. Turn off the mixer and add the coconut cream, powdered sugar and vanilla. Whip until stiff peaks form.
Spread the frosting over the cake and garnish with the toasted coconut chips. Store loosely covered in the refrigerator.