Preheat the oven to 350 degrees F. Flour, grease and line the bottoms of two 8-inch cake pans with parchment. Set aside.
In the bowl of a stand-up mixer, with the paddle attachment, combine the cake flour, almond meal, sugar, baking powder, cinnamon and salt. At a slow speed, add the cubed butter and mix until it resembles soft crumbs. In a bowl or measuring cup, whisk together the milk, egg whites and vanilla. Add about 1/2 of the milk/egg white mixture and continue beating for about 30 seconds. Add the remaining 1/2 of the milk/egg white mixture and beat for an additional 30 seconds or so, scrape down the sides and give it one last mix.
Divide the batter evenly between the two prepared cake pans. Using a rubber spatula, spread the batter to pan walls, smooth the tops and give the pans a gentle bang on the kitchen counter. Arrange pans at least 3 inches from the oven walls and 3 inches apart (this will help with proper cake circulation, yes this is a thing). Bake until thin skewer or toothpick inserted in the center comes out clean, 20 to 23 minutes. (If you're using nine-inch cake pans, the cake might take around 25 minutes to bake, just keep that in mind.)
Let cakes rest in pans for 3 minutes. Loosen from sides of pans with a knife, if necessary, and invert onto wire racks. Reinvert onto additional wire racks. Let cool completely,