Preheat oven to 350°F. Line two 9 inch round cake pans with parchment paper, then butter and flour them.
Whisk the flour, baking powder, baking soda, spices and salt together in a large bowl. Set aside.
In large mixing bowl with paddle attachment, blend the brown sugar, applesauce, oil, eggs and vanilla extract until combined.
With mixer on low speed, add ½ of the flour mixture and blend until combined. Blend in buttermilk and then add remaining flour mixture and blend until just combined.
Pour the batter evenly in the two cake pans and bake for 28-32 minutes or until a toothpick inserted in the center comes out clean. Remove and let cool for 5 minutes in pan. Run knife round edges of the pan and invert on cooling racks. Let cool completely before using.
To make the buttercream frosting, add 2 sticks butter to a skillet and set over medium heat. Allow the butter to brown lightly until it smells toasted, about 2-3 minutes. Remove from the heat and transfer the butter to the mixing bowl, letting it cool until it is at room temperature.
Add the remaining stick of butter, mascarpone, powdered sugar and salt and beat the butter and powdered sugar together until the butter is light and fluffy. Add the vanilla and beat until combined.
To assemble, place one cake layer on a serving plate. Spread ¼ of the buttercream over the cake. Add dried figs and chopped pistachios. Top with 2nd cake layer and frost the top and outside of the cake. Place sliced figs on top. Chill for 30 minutes. Serve, or store in the fridge for up to 2-3 days.