Preheat the oven to 350°F.
In a medium mixing bowl, whisk to combine the flour, cinnamon, cream of tartar, baking powder and salt.
In a large mixing bowl, combine the sugar, cooled butter, vegetable oil, egg, and vanilla extract. Whisk vigorously for 1 minute until the mixture thickens slightly and lightens in color. Whisk in the milk and sour cream until completely combined.
Add the flour mixture and whisk just until the flour is moistened and the batter is smooth.
Line a 12-cup muffin pan with paper liners. Divide the batter evenly amongst the liners, about ¼ cup in each, until they are about three-quarters full.
Bake for 20 to 22 minutes, until the tops of the cupcakes are set and spring back when pressed.
Let cool in the muffin pan for 5 minutes, then transfer to a cooling rack to cool completely.
Meanwhile, in the bowl of a stand mixer fitted with a paddle attachment, cream the butter, cream cheese and salt on medium speed for 2 minutes or until creamy.
Add the vanilla, cinnamon, and 1 tablespoon of heavy cream. With the mixer on low speed, gradually add the confectioner’s sugar. Beat on low speed for 1 minute, just until combined. If the frosting feels dry, mix in the remaining heavy cream, 1 tablespoon at a time.
Increase the speed to medium and beat for 2 minutes until fluffy and creamy.
Transfer to a piping bag fitted with a closed star tip. Pipe about ¼ cup of frosting on top of each cupcake.
Sprinkle the tops of the frosted cupcakes with cinnamon sugar and serve.
