Chocolate Cake: Heat oven to 350°F Wrap coconut in a kitchen towel, and place in the oven for 15 minutes or longer. Remove from oven, and place on a work surface. Reduce oven temperature to 300°F Tap coconut with a hammer until it cracks in several places; break it in pieces (The white flesh should be slightly pulling away from hard shell). Carefully peel, keeping pieces of coconut as large as possible. Using a vegetable peeler peel largest pieces of coconut into long curls, and place on a baking sheet for 15 to 20 minutes, until just dry. Grate the smaller pieces on the box grater. You will need about 1/2 cup grated coconut for the cake filling. Heat oven to 400°F Line a 12x17 inch jellyroll pan with parchment paper and set aside. In a bowl of an electric mixer fitted with the whisk attachment, beat egg yolks on high speed until pale yellow, 4-5 minutes. Transfer to bowl, and set aside. Wash and dry mixer bowl. Place egg whites in bowl of electric mixer fitted with the whisk attachment on medium speed until soft peaks form, 1-2 minutes. Increase speed to high, and add sugar gradually, whipping until stiff peaks form. Transfer mixture to a large bowl. Using a rubber spatula, fold egg-yolk mixture into egg-white mixture; add cocoa powder and flour over top, and gently fold together. Pour batter into prepared pans; smooth top with an offset spatula. Bake until cake springs back when touched, 9-10 minutes. Remove from oven, and immediately turn cake out onto a wire rack lined with parchment paper. Peel parchment paper from top of cake, and cool completely. Place a clean kitchen towel on work surface. Transfer cake on parchment paper to towel. Using a pastry brush, coat cake with rum. Using an offset spatula spread the white-chocolate mousse over cake. Sprinkle with 1/2 cup freshly grated coconut. With a short end of cake facing you, roll carefully into a "log" shape on a kitchen towel, and secure with clothespins or large metal binder to hold the roll in a tight round shape. Place on a baking sheet, and refrigerate until firm, at least 2 hours. Remove from refrigerator, and unwrap. Using a serrated knife, trim the ends of the roll, cutting on the bias. Choose the more presentable end, and turn it side up, on the log, forming a branch or knot. If desired, use the other cut off end as a branch. Transfer the log to a serving platter. Slide 5-inch strips of parchment paper under the log to protect the tray while decorating. Coat with Seven Minute Frosting using an offset spatula. Remove parchment pieces. Decorate with Meringue Mushrooms, Snowy Chocolate Truffles, coconut shavings, and sugared Rosemary Sprigs. White Chocolate Mousse: Dissolve gelatin in 1/4 cup cold water, and set aside for 5 minutes. Place chocolate in the bowl of a food processor, and pulse until very finely chopped. Prepare an ice water bath; set aside. Place 3/4 cup cream in a small saucepan and bring just to a boil over medium-high heat. Add gelatin, and stir to dissolve completely. Pour into food processor with the motor running and process until chocolate mixture is smooth. Transfer to medium bowl and place over ice water bath. Chill until thick enough to fall from spoon in ribbons. Whip remaining 1 3/4 cups heavy cream to soft peaks. Fold into chocolate mixture (If not using immediately, refrigerate in an airtight container). Snowy Chocolate Truffles: Heat oven to 350°F Place almonds, if using, on a baking sheet, and bake until fragrant, about 10 minutes. Set aside to cool. Use a serrated knife to spread the chocolate. Place in a heat-proof bowl; set aside. In a saucepan, bring cream to a boil. Pour directly over chopped chocolate stirring to fully incorporate. Let sit for 10 minutes. Stir until completely melted and mixed. Allow to cool for 20 minutes. Stir in almonds, if using, and place in the refrigerator until set. Use a melon baller or 1 1/4 inch ice cream scoop to portion out chocolate. Roll the scoops of chocolate between palms to form 1-inch truffles. Refrigerate until ready to serve; dust with confectioners sugar before serving. Seven Minute Frosting: In a small heavy saucepan, combine 3/4 cup sugar, the corn syrup, and 2 tablespoons water. Heat over medium heat, stirring occasionally, until the sugar has dissolved. Rub a bit between your fingers to make sure there is no graininess. Raise heat to bring to a boil. Do not stir anymore. Boil, washing down sides of pan with a pastry brush dipped in cold water from time to time to prevent the sugar from crystallizing, until a candy thermometer registers 230F, about 5 minutes. (Depending on the humidity, this can take anywhere from 4-10 minutes). Meanwhile, in the bowl of an electric mixer fitted with the whisk attachment, whisk egg whites on medium speed until soft peaks form, about 2 1/2 minutes. Gradually add the remaining 2 tablespoons sugar. Remove the syrup from the heat when the temperature reaches 230F (it will keep rising as pan is removed from heat). Pour the syrup in a steady stream down the side of the bowl (to avoid splattering) containing the egg white mixture, with the mixer on medium-low speed. Beat the frosting on medium speed until it is cool, 5-10 minutes. The frosting should be thick and shiny. Use immediately. Sugared Rosemary Sprigs: Brush washed sprigs with a glaze of white sugar from a large egg thinned with a tablespoon of water, then coat in sugar, and let air dry.