Heat oven to 350 degrees. Spray two 9-inch cake pans with nonstick spray, and line bottoms with parchment paper.

Place unpeeled bananas on a rimmed baking sheet and roast until blackened and juices have begun to seep out, about 30 minutes. Set aside to cool, then peel and set aside in a bowl. Discard peels, but add any pan juices to the bowl.

While bananas are roasting, spread coconut out on another rimmed baking sheet and toast in the same oven until golden brown, 5 to 10 minutes, stirring once. Set aside and let cool.

In a large bowl, whisk together flour, baking soda, and salt. Set aside.

In the bowl of an electric mixer fitted with the paddle attachment, mix bananas (with juices) until mashed.

At low speed, add sugars and mix to combine. Mix in eggs, one at a time, then add butter, sour cream, vanilla extract, and lime juice. Mix in flour and 1 cup toasted coconut, mixing only until just combined. (Save remaining coconut for topping cake.)

Divide batter between prepared pans and bake, rotating halfway through, until top is golden and springs back, 40 to 55 minutes. Cool in pans for 10 minutes, then unmold and transfer to a wire rack. Let cool completely.

To prepare frosting, open can of coconut cream and scoop 1/2 cup of the solid cream off the top into a measuring cup. Remaining cream can be frozen for up to 6 months.

In an electric mixer fitted with the whisk attachment, beat the butter until soft and fluffy. Beat in softened cream cheese, one chunk at a time, until mixture is very smooth. Beat in coconut cream and sugar until smooth. Beat in extract and salt. If frosting seems too soft, refrigerate 15 to 30 minutes to help it set (not longer, or it may become too firm to spread).

Spread a little less than half the frosting over one cake layer and sprinkle with half the reserved toasted coconut. Top with second layer, spread remaining frosting on top, and sprinkle with remaining toasted coconut, leaving sides of cake bare.

Note: Make sure you use unsweetened coconut cream for the frosting, and not cream of coconut, which has added sugar. If you can’t find coconut cream, substitute full-fat coconut milk: Chill a can of coconut milk, then open and measure out 1/2 cup of the solid creamy top and use that as called for in the recipe.

Yield: 12 to 16 servings