Preheat your oven to 350°F (180°C). Prepare two 8-inch round cake pans by lining them with parchment paper and setting them aside.

Using a stand mixer or hand mixer, beat the butter and oil together on medium speed until well combined. It's okay if the mixture has a few small lumps.

Add the sugar and continue to cream the mixture on medium-high speed for 3-5 minutes, until it becomes fluffy and takes on a pearly white appearance.

With the mixer on low speed, add the eggs one at a time, mixing well after each addition. Then, blend in the vanilla extract. Scrape down the sides of the bowl to ensure everything is well incorporated, and gradually stream in the buttermilk while mixing on medium speed until smooth and combined.

Add the flour, baking powder, salt, and spices to the bowl, mixing on low speed until just combined. Stop the mixer while there are still a few streaks of flour visible, then gently fold the mixture with a rubber spatula until the batter is smooth and the flour is fully incorporated.

Divide the batter evenly between the prepared cake pans. Bake in the preheated oven for 25-35 minutes, or until a toothpick inserted into the center of the cakes comes out clean with just a few moist crumbs attached.

Carefully take the cakes out of the oven and let them cool in their pans for about 10 minutes. Then, gently invert them onto a wire rack and allow them to cool completely.

Place the softened cream cheese and butter in the bowl of a stand mixer or use an electric mixer.

Beat on medium-high speed for 3-5 minutes until the mixture is smooth and creamy.

Scrape down the sides of the bowl, then gradually add the powdered sugar, mixing on low speed one cup at a time.

Once fully incorporated, add the vanilla and cinnamon. Increase to medium speed and beat until the frosting is light and fluffy.

Start by trimming the tops of the cake layers with a serrated knife if needed, to create an even surface. Spread a small teaspoon of frosting in the center of your cake board or stand to help anchor the first layer of cake in place.

Place the first cake layer on top, then generously spread about 1 cup of frosting over it, smoothing it into an even layer. Take the second cake layer, flip it upside down, and place it on top with the flat side facing up. Coat the entire cake with a thin layer of frosting, known as the crumb coat, to seal in any loose crumbs.

Chill the cake in the fridge for 20 minutes, or until the frosting feels firm to the touch. Once chilled, apply a thick, final layer of frosting to create a smooth, beautiful finish.

To complete the look, dust the cake with cinnamon and garnish with cinnamon sticks and star anise. Slice, serve, and enjoy the delightful flavors!