Preheat oven at 350-degree Fahrenheit and prepare an 8-inch round spring form cake pan by greasing it nicely.
In a mixing bowl combine oat flour, baking powder, baking soda, salt, cinnamon powder, nutmeg powder, cardamom powder and mix well with a whisk or a spoon. Keep it aside.
In another mixing bowl combine butter and sugar.With a hand electric mixer break the butter and whip up the sugar in it at the minimum speed until soft and fluffy (4-5 minutes).
Then add, vanilla extract, soaked flaxmeal and grated carrot. Whip it again with the hand electric mixer at the minimum speed (about 2-3 minutes).
Lastly, add vinegar and whip it again for 30 seconds.
Now, fold in the dry ingredients into the wet ingredients and whip it with the hand electric mixer at the lowest speed until the batter is well mixed (about 2-3 minutes).
Now, pour the cake batter at the center of the cake pan. You may use a spatula to scrape the batter from the mixing bowl. Now without tapping the cake pan just twist the cake pan making sure the batter spreads evenly through out the cake pan.
Place it in the middle rack of the oven and bake it for 30-32 minutes or until the tester comes out clean. If the cake at this point feels little undone let it bake for another 3 minutes but do not exceed baking time more than 35 minutes.
Take it out of the oven and let it cool in the cake pan for at least 1 hour. (Do not disturb the cake or else it might break or may not leave the cake pan). Once it is completely cooled the cake will become firmer and will be completely done from inside. Now, release the spring of the cake pan. Then, place a plate on top of the cake gently and turn it around. Place it on a flat surface. Now, gently try to separate the bottom of the cake pan from the cake.
Now, whip up the frosting ingredients. With the help of the butter knife spread it on the top of the cake. Garnish with chopped walnuts and crushed pistachio.