Stir graham cracker crumbs and melted butter together in a bowl; press firmly into a pie dish.
Beat eggs and white sugar together in a bowl; mix in cornstarch and cake flour.
Heat milk and cinnamon stick together in a saucepan until just under the boiling point, 5 to 10 minutes. Pour milk mixture into egg mixture, whisking constantly. Pour milk-egg mixture back into saucepan.
Cook milk-egg mixture over medium heat, whisking constantly, until mixture thickens, 5 to 10 minutes. Remove from heat and stir in 2 tablespoons butter and vanilla extract until completely incorporated.
Pour milk mixture into prepared crust and sprinkle with cinnamon sugar.