Preheat the oven to 355 degrees F or 180 degrees C. Butter a 9-inch diameter round pan and line with buttered parchment paper.
In a small saucepan over medium heat, add the butter, brown sugar, molasses and ginger. Stir until the sugar dissolves.
Combine the flours, baking soda, nutmeg and cinnamon in a large bowl.
Whisk the cream, ricotta and eggs together in a medium bowl. Add the butter mixture, then stir into dry the ingredients along with the lime zest, orange zest and coconut. Pour into the prepared pan and bake for approximately 45 minutes.
Add all the syrup ingredients to a small saucepan over low heat and stir until the sugar dissolves. Bring to a boil, then cook for 2 minutes without stirring. Keep the syrup hot.
Prepare the filling by adding the cream to a large bowl and beating with a hand mixer, until very stiff peaks form. Add the mascarpone and beat lightly. Fold in the ricotta, powdered sugar, lime zest and orange zest. Cover and refrigerate until thick.
Remove the cake from the oven. Pierce all over with a skewer, then pour the hot syrup over the cake. Cover and refrigerate, wrapped well in plastic wrap, until cold.
Run a knife around the edge of the pan and remove the cake to a cutting board or large plate. Line the pan with plastic wrap and slice the cake horizontally into 3 layers. Return 1 layer to the pan. Spread with 1/3 of the filling, top with the second cake layer and cover with another 1/3 of the filling, then top with the final cake layer. Wrap and refrigerate the cake for another couple of hours or overnight. Cover the remaining cream and refrigerate until ready to use.
When ready to serve, remove the cake from the pan to a serving plate or cake stand and frost the cake with the remaining cream. Press the shredded coconut all over the cake and serve.
A viewer or guest of the show, who may not be a professional cook, provided this recipe. It has not been tested for home use.