Cake: Preheat oven to 325 degrees. Butter a 9-by-3-inch springform pan and line with parchment. Butter parchment. Whisk together flour, baking powder, salt, and 3/4 cup granulated sugar in a bowl. Whisk together butter, egg yolks, and milk in another bowl. Whisk flour mixture into yolk mixture until smooth.
Beat egg whites with a mixer on high speed until frothy. Add cream of tartar and continue to beat until soft peaks form, about 3 minutes. Gradually add remaining 3/4 cup granulated sugar and beat until stiff, glossy peaks form, about 3 minutes. Whisk one-third of white mixture into yolk mixture. Gently but thoroughly fold in remaining white mixture.
Spread batter in prepared pan. Bake until top of cake springs back when lightly touched, 50 to 55 minutes. Slide a paring knife around edge of cake to loosen; release cake from pan. Let cake cool 15 minutes on pan base on a wire rack. Invert cake onto wire rack; remove pan base and parchment. Turn cake top-side up onto rack and let cool completely.
Assembly: With a serrated knife, split cake horizontally into 4 layers. Transfer bottom layer to a cake plate or platter. Spread with 1 cup apple butter. Add second layer; spread with 1 cup apple butter. Repeat with third layer and remaining 1 cup apple butter. Top with fourth cake layer, domed-side up. Filled cake can be stored in refrigerator up to overnight.
Beat cream and confectioners' sugar with a mixer on medium-high speed until soft peaks form, about 2 minutes. Dollop on top of cake. Sprinkle with cinnamon.