First prepare the flax "whites"by boiling the whole flax seeds with the water.
Reduce heat to a rolling simmer & let it reduce down to 1¾ - 1½ cups, this may take 20-30 minutes (or more) but it is important to get it reduced properly
Strain the mucilage through a fine sieve and it will look just like raw egg whites, if it is too liquid (meaning you have more than 1¾ cups of mucilage) you will need to return the goop & the seeds to a pot and reduce longer. *Note: It will thicken slightly as it cools
Once you have gotten to the desired consistency, discard the seeds or feed them to the birds! Or use them in your favorite whole grain bread recipes
To make the buttercream Add the granulated sugar to the hot mucilage & stir to help dissolve, if it is not dissolving place everything in a pot & cook stirring constantly until dissolved. Then cool to cold
Whip the cold mucilage/ sugar mixture on high speed with the cream of tartar until it is stiff & glossy like a meringue.
Add the sifted confectioner's sugar & mix to combine
Slowly add the softened vegan butter & shortening (*if using) while mixing on high speed
It may look as if your emulsion is starting to break, but with high speed whipping it will eventually come together! Just keep whipping!
Add the vanilla extract last
**another note on the flax "whites" if your first reduction of "goop" seems to be too thin, you can always reduce it down later by boiling it down again (without the seeds)