Begin by placing the ripe bananas in a large bowl. With a fork or potato masher, mash them until they are smooth. The peel can be left on while mashing for easier handling. Once mashed, set aside.
In a separate mixing bowl, combine the canola oil, plain Greek yogurt, and eggs. Use an electric mixer to blend them well. Add the granulated sugar, light brown sugar, vanilla extract, and lemon juice, mixing until everything is well combined and smooth.
Now, fold the mashed bananas into the wet mixture. In another bowl, whisk together the all-purpose flour, baking soda, baking powder, and kosher salt. Gradually add this dry mixture to the wet ingredients, stirring gently until just combined. Be careful not to overmix!
Gently fold in the shredded sweetened coconut into the batter, ensuring an even distribution throughout.
Pour the batter into a greased 9x13 inch baking pan. Bake in the preheated oven for 30-35 minutes, or until a toothpick inserted into the center comes out clean. Once done, remove from the oven and let it cool in the pan for about 10 minutes before transferring to a cooling rack.
While the cake is cooling, prepare the chocolate frosting. In a large mixing bowl, beat the cream cheese and butter together until creamy and smooth. Gradually add the powdered sugar and cocoa powder, mixing until fully incorporated. Pour in the coconut cream and vanilla extract, beating until the frosting is fluffy and spreadable.
Once the cake has completely cooled, spread the chocolate frosting generously over the top using a spatula. For an extra touch, sprinkle additional shredded coconut on top of the frosting.