Add the Cinnamon Toast Crunch cereal to the milk, and stir until fully soaked; let steep for 40 minutes.

Place a fine-mesh sieve over a medium bowl and strain out the milk. Using the back of a spoon, wring the milk out of the cereal, but don't force the cereal through the sieve. Discard the soaked cereal, and set the cereal milk aside.

Preheat oven to 350ºF degrees. Line three 6-inch round cake pans with parchment paper and spray with nonstick cooking spray.

In a large mixing bowl, whisk together the flour, baking soda, baking powder, cinnamon, salt, crushed cereal, and both sugars until well combined. Add the oil, yogurt, and 3/4 cup cereal milk and continue stirring with a whisk. Stir in the egg, followed by the vanilla.

Pour batter into prepared baking pans and bake in the oven for 32-34 minutes, or until a toothpick inserted in the center comes out clean. Allow cakes to cool in the pan for 10 minutes before transferring to a wire rack to cool completely.

In the bowl of a stand mixer fitted with the paddle attachment, beat the butter and salt on high until fluffy, about 3 minutes. Add the powdered sugar, a cup at a time, until fully incorporated. Mix on high for 3 minutes. Add the vanilla, followed by the cereal milk, a Tablespoon at a time, beating until fluffy, about 2 minutes.

Remove 1 cup of the frosting and set aside for the filling. Transfer the rest of the buttercream to a separate bowl, then return bowl to mixer.

In the mixer, beat the cream cheese, reserved frosting, and crushed cereal until smooth and combined. Add half of the whipped cream, and continue beating until combined. Remove bowl from mixer, and fold in the rest of the whipped cream.

Place a cake layer on a cake plate or pedestal. Spread 1/3 of the filling on top, and repeat with the remaining cake layers and filling, ending with a layer of filling on the top. Chill cake in the freezer for 1 hour.

Once chilled and solid, frost the cake with the frosting. Coat entire cake in cinnamon sugar, then finish with a border of frosting around the top. Garnish with Cinnamon Toast Crunch pieces.