Preheat oven to 375°F. Place carrots, oil, and eggs into a blender. Blend on pulse or smoothie setting until mixture is the consistency of wet cement (about 15-30 seconds).
In a bowl, mix dry ingredients: flour, sugar and baking powder.
**(It's fine to use 2 cups of white flour instead of a white/wheat mix. I actually like the texture of whole wheat flour. I find that the taste and texture of the wheat pair really well. Nowadays my mom uses some almond flour, but the original recipe doesn't call for it.)
Pour the wet mixture into the dry, and mix with a wooden spoon until it is fully incorporated batter. Add nuts, if using nuts.
Butter all surfaces of a large baking dish, and sprinkle a few tablespoons whole wheat flour onto the butter. Shake the flour around until it sticks to all of the butter. Throw out any excess flour. Pour cake batter into the baking dish. Sprinkle the top of the batter with cinnamon and sugar. Add nuts for decoration.
Cover with foil and bake for about 20-25 minutes covered, and 5-10 minutes uncovered, depending on how well your oven browns.