In the bowl of an electric mixer fitted with the paddle attachment, beat together butter and sugar until well combined. Add egg and mix, scraping down the sides of the bowl as necessary.
In a medium bowl, combine both flours. With the mixer on low speed, add flours all at once; mix until well combined.
Turn dough out onto work surface and form into two disks. Wrap with plastic wrap and refrigerate until chilled, at least 4 hours and up to overnight.