Line a tall 6" springform pan or a 9" springform pan with plastic wrap along the base and walls. Set aside.
Process carrots into a fine mince in a food processor. Add in all remaining base ingredients and process to thoroughly combine. Pause and scrape down sides as needed. Transfer this mixture into the springform pan. Press it down evenly and firmly all around. Then cover with a piece of parchment paper and press down with a flat-bottomed object to flatten and compress the mixture evenly. Remove the parchment, and smooth out any uneven areas with a spoon. Place the cake base into the freezer for about 4-5 hours.
Prepare frosting once the cake is chilled. Blend all frosting ingredients, except cacao and oats, together in a high power blender (use that Vitamix tamper if you have one, or pause and scrape down sides as needed). Add the cacao and oats and blend once again into as smooth a mixture as possible.
Remove cake out of the freezer and out of the plastic wrap. Optional: if making a layer cake, carefully slice the cake in half at this point (or thaw it out a little first for easier slicing). Frost the cake and place back in the freezer to chill and set for about 20 minutes. Keep cake frozen and thaw out for about 20-30 minutes prior to serving. Enjoy!