Preheat the oven to 350°F. Line a 9 x 13-inch baking pan with parchment paper.
To make the batter: In a large mixing bowl, add the canola oil, eggnog, cane sugar, and eggs. Mix using a hand mixer (or stand mixer or whisk) until the eggs are combined.
Add the pastry flour, baking powder, salt, nutmeg, and vanilla bean and mix until combined into a smooth cake batter.
Transfer to the prepared baking pan and spread evenly. Bake for 30 to 35 minute or until toothpick inserted in the center comes out clean. Allow the cake to cool completely in the cake pan.
To make the frosting: In the bowl of a stand mixer fitted with the paddle attachment (or using a hand mixer), add the vegetable shortening, powdered sugar, and eggnog. Mix on low until combined and then speed mixer up to high and mix for 2 to 3 minutes or until light and fluffy.
Transfer 1/4 cup of frosting to a small bowl and add in the matcha. Mix to combine completely, add more matcha if you want a darker color. Transfer to a piping bag fitted with a coupler. I use a coupler because I’m using 4 different tips for the trees.
Add 2 tablespoons of frosting to another small bowl and add the cocoa powder and mix to combine completely. Transfer to a piping bag with tip #12.
Spread the remaining white frosting onto the cake evenly.
Using the green frosting, start with Ateco tip #21 first, pipe a zigzag triangle of frosting for a tree. Add a small line with the brown frosting did the trunk.
Continue to do this all over the cake, anywhere you want trees. This can be totally freeform, have fun with it! I did one tree per slice, so 12 trees on the cake (3 across and 4 down). I used Ateco tip #21, #6, #101, and #15 for zigzag triangles. I also used Ateco tip #21 and piped dollops in the shape of a triangle. And last, I used Ateco tip #21 to pipe rosettes in the shape of a triangle for 5 different types of trees. You can use all these methods, or even just one of them! (See the video for exactly how I pipe them).
Store extra cake in an airtight container in the fridge for up to 3 days.