For the carrot cake, preheat the oven to 180C/350F/Gas 4. Line the base of a 23cm/9in round springform cake tin with re-usable non-stick silicone liner or baking parchment and grease the sides with olive oil.
Toast the pine nuts by browning in a dry frying pan; the oven alone is not enough to scorch out the paleness. Set aside.
Grate the carrots in a processor (for ease) or with a coarse grater, then sit them on a double layer of kitchen paper and wrap them, to soak up excess liquid. Set aside.
Put the golden sultanas in a small saucepan with the rum, bring to the boil, then turn down and simmer for 3 minutes.
Whisk the sugar and oil until creamily and airily mixed.
Whisk in the vanilla extract and eggs and, when well whisked, fold in the ground almonds, nutmeg, grated carrots, golden sultanas (with any rum that clings to them) and, finally, the lemon zest and juice.
Scrape the mixture into the prepared cake tin and smooth the surface with a rubber spatula. The batter will be very shallow in the tin.
Sprinkle the toasted pine nuts over the cake and put it into the oven for 30–40 minutes, or until the top is risen and golden and a skewer inserted into the centre comes out sticky but more or less clean.
Remove from the oven and let the cake sit in its tin on a wire rack for 10 minutes, then unspring and leave it on the rack to cool.
For the mascarpone cream, mix the mascarpone with the icing sugar and rum.
To serve, transfer the cake to a plate. Put the mascarpone cream in a bowl to spoon alongside the cake, for those who want.