Preheat your oven to 350°F (175°C) and line two cookie sheets with silicone baking mats.
Make the Cookie Dough
In a stand mixer, cream together the butter, oil, granulated sugar, and powdered sugar until smooth. Add in the egg and heavy whipping cream, mixing until fully incorporated. In a separate bowl, whisk together the flour, cornstarch, salt, and baking powder. Gradually add the dry ingredients to the wet ingredients until a dough forms.
Weigh 2.2 oz portions of dough for even-sized cookies, if desired. Roll each portion into a ball, place on the cookie sheet, and press into thick disks. Arrange six cookies per tray for even baking.
Bake for 10 minutes. Let the cookies cool completely before frosting.
Make the Vanilla Buttercream Frosting
In a stand mixer, beat the softened butter, powdered sugar, heavy whipping cream, and vanilla extract until smooth and creamy. Divide the frosting between two bowls, adding red gel food coloring to one and green to the other.
Using a cookie scoop, add a dollop of frosting to each cookie. Press each cookie upside down on the silicone mat to spread the frosting evenly. Repeat with the remaining cookies and colors.
Place the frosted cookies in the freezer for 10 minutes to set the frosting.
Gently peel the cookies off the silicone mat, then sprinkle with Christmas-themed sprinkles for a festive finish.