Soak figs in whiskey in a bowl for at least 30 minutes.

Preheat the oven to 350 degrees F (175 degrees C). Line a 12-cup muffin tin with paper liners.

Combine flour, baking powder, baking soda, salt, cinnamon, cream of tartar, and cloves in a bowl.

Blend white sugar, oil, and brown sugar together in a separate bowl using an electric mixer. Add egg and mix until creamy. Mix in buttermilk and vanilla extract. Reserve 1 tablespoon of fig mixture for frosting, and mix remainder into batter. Beat in flour mixture until just combined.

Spoon batter into the prepared muffin cups, filling each 2/3 full.

Bake in the preheated oven until a toothpick inserted into the center of a cupcake comes out clean, 15 to 20 minutes. Remove from the oven and transfer to wire racks to cool completely, about 30 minutes.

Beat cream cheese and shortening together in a bowl using an electric mixer until creamy. Add powdered sugar slowly, 1 cup at a time, until creamy. Add vanilla extract. Slowly drizzle in reserved fig mixture; mix frosting until combined.

Pipe frosting onto cooled cupcakes.