Preheat oven to 325°F. Spray two 6-inch round cake pans with nonstick spray, line with parchment paper, and spray again. Set aside.
In a medium-sized bowl, whisk together flour, baking powder, salt, and cinnamon. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, cream the butter and sugar on medium-high speed until pale and fluffy, about 5 minutes.
With the mixer on low, add the egg whites one at a time, scraping the bowl between each addition and mixing well after each (about 30 seconds).
Add the vanilla extract and sour cream, mixing on low just until combined. (It may look curdled, but don’t worry! The flour will even it out.)
With the mixer on low, add one-third of the dry ingredients and mix just until combined. Add half of the buttermilk, mix, and then add another third of the dry ingredients. Follow with the remaining buttermilk, mix for 10 seconds, and then add the rest of the dry ingredients. Do not overmix.
Divide batter evenly between the prepared pans. Use a kitchen scale for precision if you like, and an offset spatula to spread the batter evenly.
For the Cinnamon Swirl: Mix the brown sugar, flour, and cinnamon until combined. Add the melted butter and mix just until it forms a smooth mixture. Immediately drop small spoonfuls of the cinnamon swirl onto the cake batter, then gently swirl with a knife or toothpick.
Bake for 28-32 minutes, or until a toothpick inserted into the center comes out with a few moist crumbs.
Cool for 10-20 minutes before transferring the cakes to a cooling rack. Cool completely before wrapping with plastic wrap and refrigerating if not using until the next day.
For the Brown Sugar Cinnamon Buttercream:
In the bowl of a stand mixer fitted with the paddle attachment, beat the butter and cream cheese on medium-high speed until creamy, about 3 minutes. Scrape down the sides of the bowl as needed.
Add the brown sugar and beat on medium-high speed until combined, about 1 minute.
Add the cinnamon, powdered sugar, heavy cream, vanilla extract, and salt. Turn the mixer on low speed and mix just until combined, about 30 seconds. Then increase the speed to medium-high and beat until creamy and smooth.
Use a rubber spatula to beat out any air pockets, making the frosting extra smooth.
Assembly:
Place a small dollop of buttercream in the center of your cake board to act as glue. Place the first cake layer (top side up) onto the cake board.
Spread a little over half a cup of buttercream evenly on top of the first layer. Make sure the frosting is level by getting eye-level with the cake.
Add the second cake layer, top side down, onto the frosted layer. Spread another even layer of buttercream on top.
Place the third cake layer, top side down, on the second frosted layer. Repeat with another layer of buttercream.
Crumb coat the entire cake with a thin layer of buttercream and chill for 15 minutes.
Frost the cake with the remaining brown sugar cinnamon buttercream. For the best flavor and texture, serve the cake at room temperature.