Preheat the oven to 350 degrees F.
Line the bottom of three (8-inch) cake pans with parchment paper and grease the sides.
In the bowl of a stand mixer fitted with the paddle attachment, add 3/4 cup of the unsalted butter and the granulated sugar, creaming them together on medium speed until light and fluffy, about 3-4 minutes.
Add the sour cream and 2 teaspoons of the vanilla to the butter mixture and mix until combined.
Add 3 of the egg whites to the butter mixture and mix until well-combined.
Add the remaining 3 egg whites and mix until well-combined.
Scrape the sides of the bowl as needed to make sure everything is combined.
In a medium bowl, add the flour, the baking powder, 1 teaspoon of the cinnamon, the salt and whisk to combine.
In a small bowl, add 3/4 cup of the milk and 1/4 cup of the water.
With the stand mixer on low speed, add 1/2 of the flour mixture to the butter mixture and mix until combined.
Add the milk mixture to the butter mixture and mix until combined.
Add the remaining flour mixture to the batter and mix until smooth, scraping the sides of the bowl as necessary.
Divide the batter evenly among the prepared cake pans.
Bake the cakes until a toothpick inserted into the center of the cakes comes out clean, about 23-25 minutes.
Allow the cakes to cool in the pans for 2-3 minutes.
Transfer the cakes to wire racks to cool completely.
Clean out the bowl of the stand mixer and the paddle attachment.
In the bowl of the stand mixer fitted with the paddle attachment, add 1 1/2 cups of the salted butter and the shortening and beat together on medium speed until smooth.
Slowly add in 6 cups of the powdered sugar and mix until smooth.
Add the remaining vanilla, 1 teaspoon of the cinnamon, and the remaining milk to the butter mixture and beat until smooth.
Slowly add in 6 cups of the powdered sugar and mix until smooth, scraping the sides of the bowl as necessary until a frosting forms.
In a small bowl add the remaining powdered sugar, the brown sugar, 1 tablespoon of the cinnamon, and the remaining water and whisk until smooth. Set the glaze aside.
Using a large serrated knife, carefully remove the domes of the cakes so that they are flat.
Place the first cake on a serving plate and spread 2 1/2 tablespoons of the cinnamon sugar glaze over the cake layer.
Allow the glaze to soak into the cake.
Spread 1 cup of the frosting on top of the cake.
Place the second cake on top of the first cake and repeat the glaze-soaking and frosting processes.
Add the third cake on top of the second cake and repeat the glaze-soaking and frosting processes.
Frost the sides of the cake with the remaining frosting and optionally pipe decorations on the sides and top of the cake.
Slice and serve dusted with the extra cinnamon.