Preheat the oven to 350°F Line the bottom of a 9" springform pan with a nonstick silicone liner or baking parchment. Grease the liner and sides of the pan with olive oil. Place the pine nuts in a small dry pan and toast them over low heat, shaking often.
Wrap the grated carrot in a double layer of kitchen towels. Twist the towels around the carrots to remove liquid.
Put the raisins in a small saucepan with the rum, and bring to a boil over medium heat. Lower the heat and simmer for 3 minutes.
Whisk together the sugar and 1/2 cup of oil until creamy. Add vanilla and eggs and whisk until combined. Fold in the ground almonds, nutmeg, grated carrots, raisins and rum, and finally the finely grated lemon zest and lemon juice.
Transfer batter into the prepared springform and smooth the surface with a rubber spatula. The cake will be fairly thin. Sprinkle the pine nuts over the top.
Bake in preheated oven until the top is risen and golden and a cake tester comes out sticky but otherwise more or less clean, just one or two moist crumbs clinging to it, 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.
Beat together the mascarpone, confectioners' sugar and rum in a small bowl. Slice the cake and serve with the mascarpone cream.