Preheat oven to 350°F. Generously grease two 9-inch cake pans with shortening, then dust with flour. Shake out the excess flour and set pans aside.

Place the cake mix, milk, melted butter, eggs, vanilla, and cinnamon in a large mixing bowl. Blend with an electric mixer until well combined. Divide the batter evenly between the two pans, smoothing it out with a rubber spatula. Place the pans in the oven side by side.

Bake the cakes until they are golden brown and spring back when lightly pressed with your finger, 27-29 minutes.

Remove the pans from the oven and place them on wire racks to cool for 10 minutes. Invert each onto a cooling rack, then invert them again so the cakes are right-side-up. Allow them to cool completely, about 30 minutes.

Meanwhile, prepare the frosting by placing the butter in a large mixing bowl. Blend with an electric mixer on low speed until fluffy, 30 seconds. Stop the mixer and add the powdered sugar, 3 tbsp. milk, vanilla, and cinnamon. Beat with the mixer until light and fluffy. Blend in up to 1 tbsp. milk if the frosting seems stiff.

Place one cake layer, right side up, on a serving platter. Spread the top with frosting. Place the second layer of cake on top of the first and frost the top and sides of the cake with clean, smooth strokes.

If desired, top with crumbled Snickerdoodle cookies.

Place the cake, uncovered, in the refrigerator until the frosting sets, about 20 minutes.