Preheat the oven to 350 degrees F. Line the base of the springform pan with a nonstick silicone liner or baking parchment. Grease the sides with olive oil. Add the pine nuts to a small dry pan and toast them over low heat.
Grate the carrots in a food processor or with a coarse grater, and put them on a double layer of kitchen towels. Wrap the towels around the carrots to soak up the excess liquid.
Put the sultanas in a small saucepan with the rum, and bring to the boil over medium heat. Lower the heat and simmer for 3 minutes.
Whisk the sugar and 1/2 cup of oil in a stand mixer or by hand, until creamily and airily mixed together.
Whisk in the vanilla and eggs in a large bowl. Fold in the almond meal/flour, nutmeg, grated carrots, golden sultanas (and any rum that clings to them) and finally the lemon zest and lemon 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 with the pine nuts and bake until the top is risen and golden and a cake tester comes out sticky but otherwise more or less clean, about 30 to 40 minutes.
Remove the cake from the oven and let it sit on a rack for 10 minutes before removing the sides. Let cool until ready to serve. Transfer the cake to a serving platter.
Combine the mascarpone, confectioners' sugar and rum in a small bowl. Slice the cake and serve with the mascarpone cream.
Make Ahead Note:
The cake can be baked up to 3 days ahead. Wrap tightly in plastic wrap and store in airtight container in a cool place. Will keep for a total of 5 to 6 days.
The cake can be frozen (still on base of the tin), carefully wrapped in double layer of plastic wrap and 1 layer of foil, for up to 3 months. Defrost overnight at room temperature.