Heat the oven to 180C (160C fan)/350F/gas mark 4, and oil or spritz a 23 cm round cake tin with oil or cooking spray, then line it with greaseproof paper.
Put the chopped carrots in a food processor and pulse until finely shredded.
In a small bowl, whisk the flour, baking powder, bicarb, salt, cinnamon, cardamom and nutmeg.
In a large bowl, whisk the granulated sugar, oil, eggs and vanilla until combined.
Add the shredded carrots and whisk for about two minutes more, until airy and light.
Whisk in the flour mixture a third at a time until just incorporated, then pour the batter into the lined tin.
Bake for 25-35 minutes, until golden brown and the centre springs back when touched.
Leave the cake to cool in its tin for 15 minutes, then invert on to a plate and carefully peel off the paper.
Invert the cake again on to a rack and leave to cool.
In the bowl of a stand mixer fitted with the whisk attachment, beat the cream on medium speed for four to five minutes, until it forms stiff peaks.
Transfer the whipped cream to a small bowl and chill until ready to use.
In the same bowl of the stand mixer, this time fitted with the paddle attachment, mix the cream cheese, vanilla and salt on medium speed for about a minute, until smooth.
Add the icing sugar and mix until smooth.
Using a rubber spatula, gently fold a little of the whipped cream into the cream cheese mixture until incorporated, then fold in the remaining whipped cream.
Transfer the cake to a serving plate, dollop the cream cheese mousse on top and smooth with an offset spatula.
Dust with cinnamon and serve immediately.
