Preheat the oven to 350°F. Grease 3, 6-inch cake pans (or 2, 8-inch cake pans) and line with parchment paper. Set aside.
Whisk the flour, xanthan (if using), baking powder, baking soda, cinnamon, allspice, ginger and brown sugar together in a large bowl. Add the prune puree, buttermilk, oil, and eggs and whisk well until the batter is smooth. Stir in the grated carrots and vanilla extract.
Evenly distribute the batter between the pans and tap them on the counter a few times to settle the batter. Bake for about 20-25 minutes, or until they spring back in the middle when lightly pressed, or a toothpick inserted in the middle of the cake comes out clean. Remove from the oven and cool in the pan for a few minutes. Run a sharp knife around the edge of the cakes and carefully invert them onto a cooling rack. Cool completely.
Make the buttercream. Beat the cream cheese with the butter in a large bowl until light and fluffy. Add half of the sugar and mix lightly to combine. Pour in the milk and beat until the buttercream is smooth. Add the remaining sugar, vanilla, and sea salt. Beat until the frosting is smooth and spreadable. If it seems too stiff, add another tablespoon or 2 of milk.
Once cakes are cool, frost as desired. Store in the fridge for up to 3 days.