To the bowl of a stand mixer fitted with the paddle attachment (or large mixing bowl and electric mixer) combine the butter, cream cheese, egg, vanilla, and beat on medium-high speed until creamed and well combined, about 5 minutes.
Preheat oven to 350F, line a baking sheet with a Silpat or spray with cooking spray. Place dough mounds on baking sheet, spaced at least 2 inches apart (I bake 8 cookies per sheet). If you had a hard time getting dough into neat mounds before chilling, take time now to smooth them out.
Bake for 13 to 15 minutes, or until edges have set and tops are just set, even if slightly undercooked and glossy in the center. Cookies firm up some as they cool. Allow cookies to cool on baking sheet for about 10 to 15 minutes before serving. I let them cool on the baking sheet and don't use a rack. Note that baking time is longer than for most cookies due to the very moist and wet nature of the dough and the size of the cookies. If you rolled your cookies smaller, reduce baking time accordingly.
Cookies will keep airtight at room temperature for up to 1 week or in the freezer for up to 6 months. Alternatively, unbaked cookie dough can be stored in an airtight container in the refrigerator for up to 5 days or in the freezer for 4 months, so consider baking only as many cookies as desired and save the remaining dough to be baked in the future when desired.
one 18.25-ounce box red velvet cake mix, sifted (don't skip sifting or you'll have lumps that won't incorporate; if the brand of cake mix you use is slightly larger, that's fine, but smaller is not okay or the dough will be too wet)