First, let's make the candied clementine slices. In a large shallow pan, combine the white sugar and water. Turn heat on medium and stir until sugar has dissolved.
Add in three thinly sliced clementines in a single layer. Turn heat onto medium-low and allow the slices to slowly caramelize and candy. This will take 30-40 minutes. You want the liquid to be at a low simmer, not boiling. Flip the slices over occasionally.
When ready, the slices will appear almost see-through due to the sugar. Place in a single layer on a piece of parchment paper or wax paper, and allow to cool completely. Save the clementine syrup for another recipe!
Next, make the cake. Preheat oven to 350F and spray three 6" round cake pans with nonstick baking spray. In a small bowl, whisk together the ground flaxseed with the water and set aside to thicken.
In the bowl of a stand mixer, combine the flour, baking powder, baking soda, salt, and sugar.
Add in the vegan butter, and beat on low until it's incorporated and has a sandy texture.
In a small bowl, whisk together the oil, flaxseed mixture, nondairy yogurt, clementine zest and vanilla extract, and add them to the dry ingredients. Mix until combined.
Pour in the unsweetened nondairy milk and clementine juice, and beat on medium-low until smooth and creamy. Finally, gently stir in the cranberries.
Divide batter evenly among the 3 pans, and bake for 30-35 minutes until cake is set in the center and a toothpick comes out clean.
When the cakes are completely cooled, you can make the frosting. In the bowl of a stand mixer, beat the shortening, vegan butter, clementine zest, salt, and vanilla extract together until completely smooth and creamy. Add in the powdered sugar, 1 cup at a time, until a thick frosting forms. You might not need all the sugar, and you may need to add a splash of nondairy milk if the frosting is too thick.
To assemble the cake, first level the cakes (to make a flat top) if needed. Place one cake piece on your cake stand or platter, and spread some frosting on top. Repeat with all.
Pipe the remaining frosting around the edges of the cake, starting at the bottom and working your way up. Using a bench scraper, smooth the edges of the cake.
For the top, spoon any remaining frosting in a piping bag fitted with a wide star tip (such as 4B). To make the braided effect, pipe short lines of frosting and slightly overlap them as you go around the edge of the cake. Finish decorating with your cooled candied clementine slices and fresh cranberries as desired. Enjoy!