Position the oven rack in the middle and preheat the oven to 350ºF (177ºC). Grease and flour two 8" or 9" round cake pans or use homemade cake release.
In a large bowl, using a handheld mixer or a stand mixer fitted with the paddle attachment, combine flour, cornstarch, sugar, baking powder, and salt. Mix on low speed until thoroughly combined.
Add softened butter to the dry ingredients and beat on low speed until the mixture resembles sand. Scrape down the sides and bottom of the bowl with a spatula.
In a large container with a spout, gently mix together the room temperature heavy cream, egg whites, and vanilla extract until blended.
With the mixer on medium-low speed, gradually add half of the milk mixture (about 1 cup) to the dry ingredients and mix until combined. Then add the remaining milk mixture and beat again until everything is incorporated.
Turn off the mixer, scrape down the sides and bottom of the bowl, then increase the mixer speed to medium and beat the batter for about 30 seconds until smooth.
Divide the batter evenly between the prepared cake pans. Bake for 28-32 minutes or until a toothpick inserted into the center comes out clean and the tops are lightly browned.
Remove from the oven and allow the cakes to cool completely in the pans on a wire rack before removing and assembling.