Preheat oven to 350F (175C) and line a 12-count cupcake tin with paper liners. Set aside.
In a large bowl, combine butter, sugar, and oil and use an electric mixer to beat together until light and creamy and well-combined.
Add eggs and vanilla extract and stir well.
In a separate bowl, whisk together cake flour, cream of tartar, cinnamon, baking soda, and salt.
Now stirring by hand, alternate adding the dry ingredients and buttermilk to the butter mixture, starting and ending with the dry ingredients. I usually add the dry ingredients in 3 parts and the buttermilk in 2. Stir by hand using a spatula, the batter should be mostly smooth and combined, avoid over-mixing as this will make the cupcakes dry.
Evenly divide batter into prepared cupcake tin and transfer to 350F (175C) oven. Bake for 17 minutes or until a toothpick inserted in the center of a cupcake comes out clean or (preferably) with moist crumbs.
Allow to cool in cupcake tin for 8-10 minutes then carefully remove to a cooling rack to cool completely. Allow cupcakes to cool completely before covering with frosting.
Combine butter, cream cheese, and brown sugar in a large bowl and use an electric mixer to beat together until smooth and creamy.
Gradually, with mixer on low speed, add powdered sugar until combined.
Scrape down the sides and bottom of the bowl and stir in cinnamon and vanilla extract.
Add heavy cream and slowly increase speed to high. Beat for 15 seconds on high speed until frosting is smooth and light. Taste-test and add ¼ teaspoon salt if needed (this helps to cut the sweetness of the frosting).
Spread or pipe frosting over cooled cupcakes. I used an Ateco 848 piping tip to frost the cupcakes in the photos and video.