Wash, peel, and chop the carrots into 2-3 inch wedges. Grate them in a blender until finely chopped, being careful of any big chunks that may get caught in the blade. (This step can be done ahead of time.)
Preheat oven to 325 degrees. Grease and flour 2 9-inch round cake pans.
Prepare the flax eggs in a large mixing bowl and let sit. Add the sugar and oil; stir well to combine.
Add ½ of the remaining dry ingredients; stir well.
Add the carrots, then the rest of the dry ingredients until well mixed.
Divide the batter evenly between the two pans and bake until golden brown. The cake will bounce back slightly when it’s done. Let cool completely.
While the cake is baking, prepare the frosting. Bring the vegan butter and cream cheese to room temperature or until just warm enough to blend easily. Cream them together, adding the pecans and vanilla. Add the sugar in small batches (to avoid a mess!), and stir very well until combined and smooth. Refrigerate the frosting until the cake is cool.
Frost the cake with a generous layer between the two cakes. Place the pecan halves around the edge of the cake if desired.
Keep the cake refrigerated until ready to serve.