Preheat the oven to 350 degrees F. Line three 8-inch cake pans with parchment paper circles and spray with baking spray or brush with cake release.
In a large mixing bowl, whisk together the flour, sugar, baking powder, baking soda, and salt.
3 cups (384g) cake flour, 2 cups (400g) granulated sugar, 2 1/2 teaspoons baking powder, 1/2 teaspoon baking soda, 1 teaspoon salt
With an electric mixer running on low speed, add one tablespoon of the softened butter at a time, mixing well until incorporated before adding another tablespoon of butter until all of the butter has been added. The mixture should look sandy and dry with coarse crumbs.
1/2 cup (113g) salted butter
Add the oil and continue to mix on low speed until the flour mixture has been evenly moistened. Add the eggs, buttermilk, and vanilla extract, mixing and stopping to scrape the bottom and sides of the bowl until evenly combined.
1/2 cup (118ml) vegetable oil or canola oil, 1 1/3 cups (315ml) buttermilk, 3 large eggs, 1 Tablespoon pure vanilla extract
Divide the cake batter evenly between the prepared cake pans. In a small bowl, stir together the sugar and cinnamon, then set aside half of this mixture for later (about 3-4 Tablespoons). Sprinkle the remaining 3-4 Tablespoons of cinnamon-sugar mixture evenly over the cake batter. Use a butter knife to lightly swirl the cinnamon sugar mixture into the cake batter.
6 Tablespoons granulated sugar, 1 1/2 Tablespoons ground cinnamon
Bake for 28 to 30 minutes or until a toothpick or skewer inserted into the center of each cake layer comes out clean with just a few crumbs clinging to it. Cool completely before assembling the cake. These can be made up to 2 months in advance and wrapped tightly in plastic wrap, then frozen until ready to thaw and assemble the cake.
To make the crumbs, combine the flour, granulated sugar, brown sugar, baking powder, and salt in a large bowl. Add the oil and vanilla, then mix until evenly moistened. Squeeze handfuls together to form large clumps, then spread them evenly on a baking sheet lined with parchment paper, breaking them up into clusters of varying sizes. Bake at 350 degrees F for 10-12 minutes (I do it right after removing the cake layers from the oven), until golden brown and crunchy. Immediately sprinkle the crumbs with the remaining 3-4 Tablespoons of cinnamon sugar mixture while still warm. The crumbles will firm up more as they cool. These can be made 1-2 days in advance and stored in an airtight container until ready to assemble.
1 cup (200g) granulated sugar, 1 1/2 cups (192g) cake flour, 4 Tablespoons brown sugar, 1 teaspoon baking powder, 1 teaspoon salt, 1/2 cup vegetable oil, 2 Tablespoons pure vanilla extract
To make the frosting, beat the butter and cream cheese together in a large mixing bowl until completely combined and smooth. Add the brown sugar and beat again for 1 minute. Add the powdered sugar, cinnamon, and vanilla, then mix just until smooth and combined. It should be light, fluffy, and spreadable, but do not overmix or the frosting can become runny.
1 cup salted butter, 8 ounces cream cheese, 1/2 cup light brown sugar, 5 1/2 cups powdered sugar, 2 teaspoons ground cinnamon, 2 teaspoons pure vanilla extract
To assemble, level off the cake layers if needed. Place one layer on a cake plate and spread with about 1 1/2 cups of the frosting. Sprinkle with a generous amount of the cooled snickerdoodle crumbles. Repeat with the remaining cake layers and frosting. Use some of the frosting to lightly frost around the edges of the cake to seal in moisture, then pipe a decorative swirl around the top edge of the cake using a piping tip (I used the Wilton 1M tip). Pile as many remaining cookie crumbles on top as you like. Freeze the entire cake for 20 minutes or refrigerate 1 hour to help set the frosting before slicing and serving.