Preheat your oven to 350°F and generously grease and flour your bundt pan.
In the bowl of a stand mixer, combine the shortening (or butter), butter, sugar, and vanilla extract. Beat on medium-high speed until the mixture becomes light and creamy, which usually takes 3-5 minutes.
Add the oil, flour, eggs, and buttermilk to the mixture. Mix on low speed until just combined. Stir in the instant pudding, flour, cream of tartar, baking soda, and salt. Mix on low until everything is well combined.
Pour the batter into the prepared bundt pan and bake for 60 minutes or until the cake turns golden brown and is baked through.
Remove the cake from the oven and let it cool for ten minutes in the pan. Place a wire rack over the base of the cake, invert the pan, and gently remove the cake. Allow it to cool for an additional 15 minutes.
In a small bowl, combine the sugar and cinnamon. Brush the melted butter over the cake and sprinkle on the cinnamon sugar mixture. You can store the cake covered for up to four days.