For the cake:
1/2 cup icing sugar, for dusting the towel and for decoration
1/2 cup sorghum flour
1/4 cup arrowroot flour
2 tablespoons quinoa flour
1/4 cup unsweetened cocoa powder (I like Hershey’s Dark)
1 3/4 teaspoons baking powder
3/4 teaspoon xanthan gum
1/8 teaspoon fine sea salt
1/2 cup plus 2 tablespoons unsweetened nondairy milk
2 tablespoons ground flaxseed
1 tablespoon coconut oil, plus more for oiling the pan
2/3 cup granulated sugar
1 teaspoon vanilla extract
2 teaspoons cider vinegar
For the filling:
1 cup full-fat canned coconut milk
8 oz (226 grams) nondairy semi-sweet chocolate chips
For the frosting:
1/2 cup nondairy buttery spread, such as Earth Balance
3/4 cup unsweetened cocoa powder, sifted
1 tablespoon vanilla extract
4 to 5 tablespoons unsweetened nondairy milk
2 1/3 to 2 2/3 cups icing sugar, sifted
To make the cake, preheat the oven to 375º F. Lightly oil a 15 x 10 x 1-inch jelly-roll pan (a baking sheet with sides). Line the bottom with parchment paper. Grease the paper with coconut oil. Dust a clean dishtowel with icing sugar, laying it out flat (you will invert the hot cake onto the dishtowel immediately after baking, so you want to have this ready.
Put the sorghum flour, quinoa flour, arrowroot flour, cocoa powder, baking powder, xanthan gum, and salt in a medium bowl. Whisk well to combine.
Put the nondairy milk, ground flaxseed, and oil in a small saucepan over medium heat. Once the mixture starts to steam and the oil is melted, whisk well to combine. Pour the mixture into the bowl of a stand mixer.
Add the sugar and vanilla to the nondairy milk mixture. Beat on high for about 2 minutes, until well combined. Turn the speed of the mixer to low. Add the flour mixture, beating until just mixed, scraping down the sides of the bowl with a spatula. Turn off the mixer and stir in the vinegar.
Spread the batter onto the prepared pan, leaving a border of about 1-inch from the sides. Bake for 9 to 12 minutes, until firm to the touch and a toothpick inserted in the cake comes out clean.
Carefully invert the cake onto the dishtowel. Peel the parchment off of the top of the cake. Starting at one of the long sides, and using the towel as an aid, gently roll the cake jelly-roll style (you will be rolling the towel inside of it). Cool completely in the towel.
As the cake cools, make the filling. Put the coconut milk in a small saucepan over medium heat. Place the chocolate chips in a heat-safe bowl. Once the coconut milk is steaming (but not boiling), pour it immediately over the chocolate chips. Let stand 10 minutes, then stir until the chocolate chips are completely melted. Refrigerate for about 1 hour until cool (it should be like pudding). Transfer the mixture to the stand mixer and whip on high for about 1 minute until the texture of mousse. Put the mixture back into the refrigerator.
Once the cake is cool, remove the filling from the refrigerator and unroll the cake, removing the towel. Spread the filling evenly over the cake to about 1-inch from the edge. Reroll the cake to form a log. Place the cake, seam side down, on a serving platter. Refrigerate while making the frosting.
To make the frosting, put the buttery spread in the stand mixer. Beat on medium-high for about 3 minutes, until fluffy and smooth. Turn the mixer to low speed. Add the cocoa powder, vanilla extract, and 2 tablespoons of the non-dairy milk. Beat until well combined. Add 1 cup of the confectioners’ sugar. Beat until smooth. Alternately add the remaining confectioners’ sugar and non-dairy milk until the mixture is smooth. Turn to high speed and beat for 4 to 5 minutes, until creamy and fluffy.
Remove the cake from the refrigerator. To make a branch coming out of the side of the log, cut a 4-inch diagonal slice off one end of the cake, placing the cut side of the piece on the side of the remaining cake. Spread the frosting over the whole cake.
Use the tines of a fork to create a rustic “bark” effect in the frosting. Dust with icing sugar for “snow”. Serve at room temperature.