Preheat the oven to 350°F (175°C). Grease three 8-inch round cake pans and line the bottoms with parchment paper; set the pans aside.
Place the whole, peel-on bananas on a parchment-lined baking sheet. Roast on the center oven rack for 20–25 minutes, until the banana skins are blackened. Remove the baking sheet and let the bananas cool until they can be handled.
When the bananas are cool enough, peel and mash them in a bowl until mostly smooth. Set the mashed bananas aside.
In the bowl of a stand mixer (or a large bowl with a hand mixer), combine 1 cup canola oil, 1 cup plain Greek yogurt, 3 large eggs, 1 cup granulated sugar, 3/4 cup light brown sugar, 1 tablespoon vanilla extract, and 2 teaspoons lemon juice. Beat on medium speed until smooth and combined, about 1–2 minutes. Add the mashed bananas and mix until incorporated.
In a separate bowl, whisk together 3 1/2 cups all-purpose flour, 2 teaspoons baking soda, 1 teaspoon baking powder, and 1 teaspoon kosher salt. Add the dry ingredients to the wet mixture and mix on low speed just until the batter is combined and no large streaks of flour remain. Do not overmix.
Fold in 1 cup shredded sweetened coconut by hand with a spatula until evenly distributed.
Divide the batter evenly among the three prepared 8-inch pans (use a scale or divide by eye). Smooth the tops and bake on the center rack for 30–35 minutes, until the cake tops are set and a toothpick inserted in the center comes out with a few moist crumbs (not wet batter).
Remove the pans from the oven and let the cakes rest in the pans for 5 minutes. Run a knife around the edges, invert each pan, and turn the cakes out onto cooling racks. Remove the parchment rounds and allow the cakes to cool completely before assembling (completely cool to the touch, about 1–2 hours).
To make the chocolate frosting: in a large mixing bowl, beat 4 ounces cream cheese and 2 sticks butter (both at room temperature) on medium speed until smooth and light, about 2 minutes.
Add 1 1/2 cups powdered sugar, 1 cup unsweetened cocoa powder, and 2 teaspoons vanilla extract. Beat on low at first to avoid a sugar cloud, then increase to medium and beat until the mixture is smooth and fluffy, about 2–4 minutes. If the frosting is too thin, add up to the remaining 1/2 cup powdered sugar (to reach 2 cups total) a little at a time until you reach a spreadable consistency.
Beat in 1/2 cup canned coconut cream until fully incorporated and the frosting is smooth. If the frosting is very soft, refrigerate it for 10–15 minutes and rewhip briefly before using.
Assemble the cake: place one cooled cake layer on a serving plate or cake stand. Spread an even layer of frosting over the top. Repeat with the second layer, then place the third layer on top and frost the top and sides of the cake with the remaining frosting.
Serve immediately or store the assembled cake in the refrigerator for up to 2 days. Bring the cake to room temperature before serving for best texture.