Snickerdoodle Cake

Preheat the oven to 350°F (177°C). Prepare three 6-inch (15-cm) or two 8-inch (20-cm) round cake pans by spraying the sides with baking spray and fitting a parchment paper circle to the bottom of each pan.
 

In a medium bowl, whisk the flour, baking powder and salt; set aside.
 

In the bowl of a stand mixer fitted with the paddle attachment, cream together the butter, oil and granulated sugar at medium-high speed for 3 minutes. Scrape the bowl and paddle. With the mixer running at low speed, add the eggs one at a time, scraping the bowl and paddle as needed. Mix just until the last egg is combined. Add the sour cream and vanilla, then beat the mixture at medium speed for 1 minute.
 

Scrape the bowl and paddle. Decrease the mixer’s speed to low. Add the flour mixture in three additions, alternating with the milk in two additions. Mix the ingredients until they are just blended. Stir the batter by hand a few times to make sure no large lumps remain.
 

Divide the batter evenly between the prepared cake pans; set aside.
 

MAKE THE CINNAMON-SUGAR RIBBON

In a small bowl, mix together the brown sugar, flour and cinnamon until they are combined. Pour the melted butter on top of the cinnamon-sugar mixture and stir the ingredients until they are just combined.
 

Add spoonfuls of the Cinnamon-Sugar Ribbon to the unbaked cakes and gently swirl it in with a butter knife. Bake the cakes for 35 to 40 minutes. They’re done when they spring back to the touch and a toothpick inserted into the centers comes out clean or with a few crumbs. Let the cakes cool in their pans for 5 minutes, then remove them from the pans and cool them on a wire rack.

In the bowl of a stand mixer fitted with the paddle attachment, cream together the butter and brown sugar at medium-high speed for about 4 minutes, until the mixture is creamy and light.
 

Decrease the mixer’s speed to low, and then add the powdered sugar 2 cups (240 g) at a time, scraping the bowl and paddle after each addition.
 

Add the cinnamon, vanilla, milk and salt and mix the ingredients together at low speed for 1 minute, until the ingredients are fully incorporated and the frosting is smooth.
 

Level the cooled cake layers to your desired height. Fill and stack the cake layers with Cinnamon–Brown Sugar Butter-cream, then crumb coat the cake with Cinnamon–Brown Sugar Buttercream. Refrigerate the cake for at least 30 minutes to allow the frosting to firm up.
 

Reserve about 1 cup (215 g) of the Cinnamon–Brown Sugar Butter-cream for step 7, then create a smooth buttercream finish with the remaining buttercream.
 

Refrigerate the cake for 20 minutes to let the buttercream set up. Meanwhile, make the Cinnamon-Sugar Topping: Place the granulated sugar and cinnamon on a rimmed medium baking sheet. Shake the baking sheet to slightly spread out the sugar and cinnamon and create an even layer for rolling (see Note).
 

When the cake has finished chilling, place a cardboard cake circle the same diameter as the cake on top of it. Run a warm paring knife around the bottom edge of the cake to separate it from the turntable, then use an angled spatula to gently lift the bottom of the cake up. Slip one hand underneath the cake. Place your other hand on the cardboard cake circle you placed on top of the cake and lift the whole thing up.
 

Turn the cake so that it is horizontal instead of vertical and gently roll the cake over the baking sheet to cover it in the Cinnamon-Sugar Topping, holding it with both hands the entire time. Keep rolling the cake, shaking the baking sheet to disperse the cinnamon sugar between rolls, until the sides are covered.
 

Place the cake on a turntable and remove the cardboard cake circle you placed on top in step 4. Add 3 to 4 tablespoons (39 to 52 g) of the Cinnamon-Sugar Topping to the top of the cake and smooth it into the buttercream with an angled spatula until the top is fully covered.
 

Use the reserved Cinnamon–Brown Sugar Buttercream to pipe a star border around the top edge with a Wilton tip 6B.