Preheat oven to 350 degrees F (180 C) and grease 2 6-count doughnut pans very well with oil. Whisk together the coconut milk, sugar, and flax seed meal in a large mixing bowl until smooth. Add the vanilla, salt, soda, and spices and mix well.
Pour in the pineapple and additional juice, then fold in the walnuts, coconut shreds, and grated carrots. Mix in the flour last until you have a very thick batter.
Divide the batter between all 12 slots in the doughnut pans (note that each slot will be piled pretty high but that's okay. Place pans in the oven and bake for 15 to 20 minutes until the tops start to brown, then remove one pan at a time and use a spoon to spread the batter in the center and clear the holes in the center of each doughnut. Repeat for the other pan then return to oven and continue baking them until the edges are very dark and the doughnuts have somewhat shrunken in size. Now remove the pans from the oven and allow to cool completely before removing the doughnuts. To loosen them once cooled, use a small spoon to gently loosen all the edges then invert the pan over a tray or cutting board to shake them loose.
For the optional icing, warm the cocnut oil for a few seconds in a small saucepan ir microwave safe bowl until just soft enough to stir. Add the maple syup, vanilla, salt, and powdered sugar and mix until smooth. Drizzle over cooled doughnuts as desired.