Preheat oven to 350°F. Line a muffin tin with cupcake liners. Combine flour, cornstarch, baking powder, cinnamon, pumpkin pie spice, and salt in a large bowl.
In the bowl of a stand mixer fitted with the paddle attachment beat oil and sugars on high speed until smooth, about 1 minute. Add pumpkin, and beat until smooth.
Beat in eggs, one at a time, mixing well after each addition. Add vanilla.
Slowly beat in dry ingredients, making sure not to overmix.
Pour batter into prepared pan, filling each cup 2/3 full. Bake 20 to 22 minutes or until a toothpick inserted into the center of a cupcake comes out clean.
Cool cupcakes completely in pan before transferring to a cooling rack. Make sure cupcakes are room temperature before frosting (not warm to the touch at all).
For the Cinnamon Cream Cheese Frosting
Add butter and cream cheese to the bowl of a stand mixer fitted with the paddle attachment. Beat on high speed until light and fluffy, about 2 to 3 minutes.
Slowly add powdered sugar, beating until smooth. Add vanilla, cinnamon, and salt.