3cups (6 sticks or 680 g)butter, at room temperature
6cups (680 g)powdered sugar, sifted
1tbspvanilla bean paste, vanilla extract, or the seeds from one vanilla bean
Preheat the oven to 350° F. Line two 12-cup muffin pans with cupcake liners and set aside.
Cream the butter, sugar, and vanilla on low speed until well combined. Increase the speed to medium and continue to cream for about 4-5 minutes, or until light and fluffy.
Reduce the speed to low and add the eggs, one at a time, beating well after each addition. Scrape down the sides and bottom of the bowl.
In a medium bowl, whisk together the flour, cornstarch, baking powder, and salt. In a measuring cup, whisk together the milk and cream.
Blend in ⅓ of the flour mixture, followed by ½ the milk/cream mixture. Blend in the second ⅓ of the flour and the rest of the milk/cream, finished by the final ⅓ of flour. Beat for just an additional 5 seconds longer to incorporate all the ingredients. Let the batter sit for 15 minutes and stir gently before scooping into muffin cups, filling ¾ full.
Bake the cupcakes for 28-33 minutes, or until a toothpick inserted into the center comes out clean.
Cool in the pans for 5 minutes before turning out onto wire rack to cool completely.
For the Buttercream
In the bowl of a stand mixer (or with a handheld mixer), beat butter until smooth and creamy. Add powdered sugar in increments with the mixer on low (so it doesn't fly out of the mixer). Add the vanilla. Turn the mixer up to medium and beat for about 5-6 minutes, or until lighter in color and texture (this extra mixing is crucial to the texture of the buttercream).