Preheat your oven to 180 degrees Celcius (356 degrees Fahrenheit).
Melt the vegan butter in a small pot on medium heat.
Peel the bananas and add them to a bowl. Use a fork to press down on the bananas. Continue this until the bananas are completely mashed.
Peel the carrots and cut off both ends of the carrots. Finely grate the carrots using your box grater.
Roughly chop the walnuts.
If you do not have ground flax seeds you can add flax seeds to your blender or food processor to grind them (pulse for about 10 seconds). Or use a mortar.
Add the shredded carrots, mashed bananas, vegan butter, chopped walnuts and all the rest of the carrot cake ingredients to a large bowl and mix well.
Take a cake pan of 20 cm (8 inches) round. Place parchment paper onto the bottom of your cake pan before locing on the side part. Then smear the sides of the cake pan with vegan butter (see picture for illustration).
Pour the mixture into your cake pan. Use a silicon spatula to make sure you get all of the dough out and spread the dough evenly in the pan, to all the outer edges.
Bake your cake in the center of the oven at 180 degrees Celcius (356 degrees Fahrenheit) for 35 minutes.
Once done, take your cake out of the oven and let it cool down in room temperature.