Step 1

For the cupcakes: Position two racks in upper and lower thirds of the oven and preheat to 350 degrees F. Line two 12-cup muffin tins with 18 cupcake liners.

Step 2

Whisk the flour, cornstarch, baking powder, salt and baking soda in a large bowl until combined. Add the butter, sugar, oil and vanilla to the bowl of a stand mixer fitted with the paddle attachment and beat on medium-high speed until light and fluffy, 3 to 4 minutes. Add the eggs and yolks one at a time, beating to blend between additions and occasionally scraping down the sides and bottom of the bowl with a rubber spatula, until completely combined and smooth. With the mixer on low, add the dry ingredients in 3 additions, alternating with the buttermilk, beginning and ending with the dry ingredients.

Step 3

Divide the batter evenly in the prepared muffin tins. Bake until a cake tester inserted into the center of the cupcakes comes out clean, rotating the tins halfway through baking time, 18 to 20 minutes.

Step 4

Cool the cupcakes in the tins on a rack for 10 minutes, then remove from the tins and cool on the rack completely.

Step 5

For the frosting: Add the butter to the bowl of a stand mixer fitted with the paddle attachment and beat on high speed until smooth, about 1 minute. Reduce the speed to low and gradually mix in the confectioners' sugar until completely smooth. With the motor running, add the heavy cream, vanilla and salt. Increase the speed to high and beat until the frosting is light and fluffy, 1 to 2 minutes.

Step 6

Transfer the frosting to a pastry bag or large resealable plastic bag fitted with a large star tip. Decoratively pipe the frosting onto the cupcakes.