Preheat the oven to 350°F. Lightly oil an 8-inch round baking pan and line the bottom with parchment paper. Set aside.

In a medium bowl, mix the all-purpose flour, baking powder, baking soda, ground ginger, cinnamon, salt, mac and nutmeg. Set aside.

In a large bowl, combine the buttermilk and extra virgin olive oil and whisk well. Add the granulated white sugar and powdered jaggery or brown sugar and whisk vigorously to start to dissolve the sugar. Whisk in one egg at a time and then continue whisking until the mixture begins to lighten in color slightly, about 3 to 4 minutes.

Stir in the vanilla and then gently fold in the dry ingredients until almost fully incorporated (it is okay if there are a few floury streaks). Add the carrots and fold in until no flour is remaining. Transfer the cake batter to the parchment-lined baking pan and tap to remove any rogue air bubbles. Bake until a toothpick comes out clean, about 42 to 46 minutes. Let the cake cool in the pan for 30 minutes, then run a paring knife between the cake and the pan and gently remove the cake from the pan. Transfer the cake to a cooling rack and let cool completely.

While the cake is cooling, prepare the frosting. Combine the heavy whipping cream and powdered jaggery in the bowl of a stand mixer. (Alternatively, you can use a large bowl and a hand mixer.) Whisk on low speed until the jaggery is mostly dissolved, about 2 to 3 minutes. Increase the speed to medium high and whip until soft peaks form, about another 2 to 3 minutes. With the machine still running, start adding the pieces of cream cheese quickly one right after the other and whip until they are fully incorporated. Transfer to a smaller bowl or container and refrigerate until ready to use.

To assemble, remove the parchment paper from the bottom of the cooled cake and transfer to a serving plate. Spread the reserved jaggery cream cheese frosting in a thick, swooshy layer on top of the cake, leaving about a ½-inch border around the edge of the cake. Decorate the top of the cake with the chopped, toasted pecans and crystallized ginger in whatever design you desire. Enjoy immediately, or refrigerate until serving.