To make the snickerdoodle cake layers

1. Prepare two 8 inch cake pans with parchment paper circles in the bottom and grease the sides. Preheat oven to 350°F (176°C).
2. Combine the flour, baking powder, cinnamon and salt in a medium sized bowl and set aside.
3. Add the room temperature butter, oil, sugar and vanilla extract to a large mixer bowl and beat together until fully creamed and light in color and fluffy, about 3-4 minutes. Do not skimp on the creaming time.
4. Add the room temperature eggs one at a time, mixing until mostly combined after each. Scrape down the sides of the bowl as needed to be sure all ingredients are well incorporated.
5. Add half of the dry ingredients to the batter and mix until mostly combined.
6. Slowly add the milk and mix until well combined.
7. Add the remaining dry ingredients and mix until combined and smooth, but do not over mix. Scrape down the sides of the bowl as needed to be sure all ingredients are well incorporated.
8. Divide the batter evenly between the cakes pans and bake for 32-36 minutes, or until a toothpick comes out with a few crumbs.
9. Remove the cakes from the oven and allow to cool for about 2-3 minutes, then remove to cooling racks to cool completely.

To make the snickerdoodle crumble 

1. Preheat oven to 350°F (176°C) and prepare a cookie sheet with a silicone baking mat or parchment paper.
2. You’ll need a total of 4 cups of cookie crumbs for the crumble and the filling. Place the cookies (about 35 medium-sized) in a food processor and pulse until crumbly.
3. Place 1 1/2 cups of crumbs in a small bowl for the crumble. Place the remaining 2 1/2 cups in another small bowl and set aside for the filling.
4. Combine 1 1/2 cups cookie crumbs, flour, sugar, cinnamon, and salt. Add the melted butter and toss until well coated.
5. Spread the mixture evenly onto the cookie sheet and bake for 6-8 minutes, or until lightly golden.
6. Remove from the oven and allow it to cool for about 5 minutes, then use a fork or something similar to toss the mixture and break it up. Allow to cool completely.

To make the snickerdoodle filling

1. Add the butter to a large mixer bowl and beat until smooth, then stir in the 2 1/2 cups cookie crumbs previously set aside for the filling.
2. Add the powdered sugar and mix until well combined.
3. Add the cinnamon, vanilla extract and salt and mix until well combined.
4. Add 1 tablespoon of milk or water to get a smooth consistency that is thicker than frosting. It should resemble the texture of cookie dough and be firm enough to cut well. Add up to 1 more tablespoon of liquid if needed to achieve the right consistency. Use your best judgment.

To make the snickerdoodle buttercream

1. Beat the butter and shortening together until smooth.
2. Slowly add half of the powdered sugar and mix until smooth.
3. Add the cinnamon, vanilla extract, salt and 2 tablespoons of water or milk and mix until smooth.
4. Slowly add the remaining powdered sugar and mix until smooth. Add additional water or milk, as needed to get the right consistency of frosting.

To put the cake together

1. Use a large serrated knife to remove the domes from the top of the cakes so that they’re flat. Next, cut each cake horizontally to make 4 layers of cake total. See my tutorial for leveling and torting a cake for additional help.
2. To build the cake, place the first layer of cake on a cardboard cake circle or a serving platter.
3. Spread about a third of the snickerdoodle filling (about 3/4 cup) into an even layer on top of the cake layer. Your filling should be thick enough that it will stay in place. If it isn’t, too much liquid was added to it and thinned it out.
4. Sprinkle an even layer of the snickerdoodle crumble over the filling, about 6 tablespoons. Press the crumble down into the filling and spread a very thin layer of buttercream frosting over the crumble so that the next cake layer will stick to it.
5. Add the second layer of cake, filling, crumble, and thin layer of buttercream. Then add a third layer of each so that you have three snickerdoodle cake layers that are exactly the same. 
6. For help moving the thin cake layers around, I find a cake lifter to be helpful.
7. Add the final layer of cake on top, then frost the outside of the cake with the remaining snickerdoodle buttercream. Refer to my tutorial for frosting a smooth cake, if needed.
8. To decorate the cake as I did, press the crumble into the sides of the cake, along the bottom third of the cake. Pipe tall swirls of frosting around the top edge of the cake (I used Ateco tip #847) and sprinkle with more crumble. Then place snickerdoodle halves evenly spaced around the top of the cake.
9. The cake is best when stored in an airtight container and eaten within 2-3 days.