Preheat the oven to 350°F. Place paper liners in every other cup of two cupcake tins. Set aside.
In a medium bowl, whisk together the gluten-free flour, cornstarch, baking powder and salt.
In the bowl of a stand mixer fitted with a whisk attachment (or use a large bowl with a hand mixer), beat the softened butter and oil together until blended well, about 3 minutes.
With the mixer running on medium-low, slowly add the granulated sugar to the oil and butter. Beat on high until the mixture is light and fluffy and turns a very pale yellow, about 3 minutes.
Add the eggs in one at a time, scraping down the bowl in between each addition. Mix in the vanilla extract, then beat on high for another 2 minutes. You want to incorporate lots of air!
With the mixer running on low, add ½ of the dry ingredients followed by ½ of the buttermilk, mixing until fully combined. Repeat with the remaining dry ingredients and buttermilk.
Using a kitchen scoop or large spoon, fill each baking cup ¾ of the way up. Bake for 18-20 minutes, until a toothpick inserted in the center comes out mostly clean with a few moist crumbs. Repeat with the remaining batter if needed.
Let the cupcakes cool in their pan for 5 minutes, then transfer to awire rack to cool completely.