Mix the sugar and cinnamon together for the swirl. Set aside.
Preheat oven to 350 degrees F. Grease and flour three cake pans and line the bottoms with parchment rounds.
Whisk the cake flour, cream of tartar, baking soda, and salt in a medium bowl.
In a stand mixer, beat the butter and sugar on medium speed for 3 minutes until light and fluffy.
Add eggs one at a time, mixing until just combined after each.
Mix in the vanilla extract.
With the mixer on low, add the flour mixture in three additions, alternating with the buttermilk in two additions, starting and ending with flour.
Divide half the batter among the three pans, sprinkle with the cinnamon sugar, then top with the remaining batter and swirl gently.
Bake for 25 to 29 minutes, until a toothpick comes out clean.
Cool in the pans for 10 minutes, then transfer to a wire rack to cool completely before frosting.
Beat the cream cheese and butter until smooth. Add powdered sugar gradually, then mix in cinnamon and salt until fluffy.
Frost between each layer, apply a thin crumb coat, refrigerate for 20 minutes, then apply the final coat of frosting.
Slice and serve, or refrigerate until ready to serve.