Place a rack in the center of the oven and preheat the oven to 350 degrees. Generously grease two 9-inch round cake pans. with solid vegetable shortening. Dust with flour, then shake out the excess flour. Set pans aside.
Place the cake mix, pudding mix, orange juice, oil, eggs and cinnamon in a large bowl. Blend with an electric mixer on low speed for 1 minute. Spot the mixer and scrape down the sides of the bowl with a rubber spatula. increase the mixer to medium speed and beat 2 minutes more, scraping down sides again if needed. the batter should look thick and well blended. Gently fold in the carrots with spatula. Divide batter between prepared pans, smoothing it out with the rubber spatula. Place pans in the oven side by side.
Bake the cakes until they are golden brown and spring back when lightly pressed with your finger, 30 to 35 minutes. Remove the pans from the oven and place them on wire racks for 10 minutes. Run a dinner knife around each layer and invert each onto a rack. Allow to cool completely before frosting.
Coarsely chop chocolate. Place in a small bowl and microwave on medium, stirring halfway through, until almost melted, 2 to 3 minutes. Remove and stir until smooth. In a large bowl, using an electric mixer,beat cream cheese with butter, lime juice and vanilla until smooth. Then beat in chocolate. Gradually beat in icing sugar until evenly mixed. 2. In a medium-size bowl, using an electric mixer, whip cream until soft peaks form when beaters are lifted. Stir one-third of whipped cream into cream cheese mixture until evenly mixed, then gently fold in remaining cream, just until no streaks remain. It's best to fill and frost cake right away. Sprinkle toasted coconut over cake. Don't refrigerate icing before using. Makes about 4 cups.