Preheat Oven and Prepare PansPreheat your oven to 325°F (163°C). Grease and line two 9-inch round cake pans with parchment paper. If using cake strips, soak them in ice water.
Mix Dry Ingredients with ButterIn the bowl of a stand mixer fitted with the paddle attachment, combine the flour, brown sugar, baking powder, salt, and all the chai spices. Cube the butter and add it to the bowl. Mix on low speed until the mixture resembles wet sand.
Add Wet IngredientsPour in the oil, milk, eggs, and vanilla extract. Mix until just combined—be careful not to overmix.
Divide and BakeDivide the batter evenly between the prepared pans. Wrap cake strips around the pans if using. Bake for 35 to 40 minutes or until a toothpick inserted in the center comes out clean. Cool the cakes on wire racks. For easier frosting, wrap the cooled cakes in plastic wrap and freeze until ready to use.
Make the FrostingIn a clean stand mixer bowl, beat the room temperature butter and cold cream cheese on high until smooth and fluffy. Reduce to low speed and gradually add the sifted powdered sugar. Increase speed and beat until smooth and creamy.
Assemble the CakePlace the first cake layer on a stand or serving plate. Spread frosting evenly on top. Add the second layer and frost the top and sides of the cake. Leave the sides semi-naked if desired. Decorate with cinnamon sticks, star anise, or a light cinnamon dusting.