Preheat your oven to 350°F/180°C. Grease and line 2 8" cake tins.
In a medium bowl, whisk together the oil, sugar, eggs, spices, vanilla, baking soda and salt together. If using a stand mixer, whisk for about 3 minutes, if doing this by hand, then whisk for about 8-10 minutes.
Fold in the flour and mix until smooth, making sure there are no flour pockets. Add in the carrots and pistachios and fold together until combined.
Pour 700g into each cake tin. Bake for 50-55 minutes, a toothpick inserted should come out clean (or with just a few crumbs). Let cool for 15 minutes, then remove from the pans and let cool completely.
Make frosting
Chill your mixing bowl for at least 1 hour, or overnight. In a stand mixer with the whisk attachment, whisk the heavy cream, salt, sugar and vanilla on medium-low for 2 minutes. The sugar needs to have completely dissolved.
Increase the speed to high and whisk for 2 minutes, until it looks very thick like Greek yoghurt.
While the mixer is running on a low speed, add in the cream cheese a tablespoon at a time. By the end, it should look like cream cheese. Turn off the mixer, and scrape the entire bowl to make sure no cream cheese is left on the side. Turn the speed to high, and whip for 3 minutes until smooth.
Notes
If you don't have a food processor to grate the carrots, grate them on the smallest side of a box grater.
If you are in the UK and your cream cheese comes in tubs, take it out of the tube and pat it down with kitchen roll beforehand to remove excess moisture.