No, not red and white in the same cookie.
I rolled some of these thick, and some of them thin. Either way, they were good. You could frost them or sprinkle with sugar, but I don't think they need it as far as flavor goes. I cut them into star shapes.
Shortbread Style Cookies
1 cup sugar
1 cup butter
3 oz cream cheese
1/2 tsp salt
1/2 tsp almond extract
1/2 tsp vanilla extract
1 egg yolk
2 1/4 cups flour
Cream the sugar with the butter and cream cheese. Add the salt, flavorings, and egg yolk, then stir in the flour. Refrigerate two hours or overnight (covered). Roll out, cut and bake 7 to 10 minutes at 375 degrees.
These could be frosted, but they taste like shortbread, so taste them after they've cooled and decide then.
I don't usually use cake mixes, and certainly not as the base for cookies, but it is a good shortcut sometimes. These come out with a pretty red color and taste like chocolate.
Red Velvet Cookies
1 box red velvet cake mix
2 eggs
1/3 cup oil
1/2 cup powdered sugar
1/2 teaspoon cornstarch
Combine the mix, eggs, and oil. Form into balls and roll in the powdered sugar that has the cornstarch stirred into it. They will spread out as they bake. Bake at 375 degrees for 8 to 10 minutes. Ideally, they should be still soft in the middle, but not raw.