I have had cookies from the following recipe. I wonder how similar this recipe is to your? They look like yours when they are done, minus the icing. The grandmother who made these (not my grannie) always made the icing pink, and now everyone in her family does as well, including her grandson.
Pink Icing Cookies
(Grandma's recipe)
1 cup shortening or margarine or butter flavored shortening (butter)
1 ½ cups sugar
2 eggs
1 cup buttermilk
1 teaspoon baking soda
1 teaspoon salt (optional)
2 teaspoons baking powder
3 cups flour
1 ½ teaspoons vanilla
¼ teaspoon lemon extract
1) Mix buttermilk and baking soda in glass measuring cup (at least 3 cup size as mixture foams and grows)- set aside
2) Cream shortening and sugar, and then add egg, vanilla, lemon, mix until smooth and creamy
3) Sift dry ingredients together (flour, salt, baking powder)
4) Mix dry ingredients into creamed mixture, alternating with milk mixture
5) Chill covered over night
6) Drop by a teaspoon onto a cookie sheet. Gluten free tend to be better if they are a little larger. Bake large sized cookies at 350 degrees for 10-15 minutes; grease and flour pan; jelly roll pan or similar thick cookie sheet works best
Icing:
½ cup of margarine or butter softened
3 ounces cream cheese softened (usually needs more so get 6 oz package)
4 cups powdered sugar
1 teaspoon vanilla
Red food coloring
1) Beat all ingredients together until smooth- may need a couple of tablespoons of milk to make right consistency for frosting but wait until after tasting to add;
2) Tasting by local experts to decide if need more cream cheese or vanilla; beat in more cream cheese and/or vanilla until tastes right; add milk if needed
3) Add a few drops of red food coloring and beat- may add more drops until desired color
4) Frost cookies generously
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and drinking a lot of 
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:swingstocking:
