Hi Colleen ~

Below are three recipes previously posted on TRL that appear to match your description. You will find more if you search for "soft sugar cookies." I hope these help. Kel
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Soft Sugar Cookies
Posted by Betsy at RecipeLink

2 cups sugar
1 cup shortening
2 eggs, beaten
1 1/2 teaspoon baking soda
2 teaspoons baking powder
2 teaspoons cream of tartar
Scant teaspoon salt
5 cups flour
1 cup sweet milk
1 1/2 teaspoons vanilla

Cream together shortening and sugar.
Add beaten eggs and mix well.
Combine dry ingredients.
Add 1/2 of the dry ingredients to the creamed mixture.
Stir in the milk and vanilla.
Add the remaining dry ingredients and mix well.
Cookies may be dropped or rolled 1/4-inch thick.
Bake on lightly greased baking sheets at 350F until lightly browned.

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Rolled Sugar Cookies
Posted by SC, FL 12/06/2001

Here is the recipe I always use. It really depends on the thickness. If you roll them the right thickness, they will be soft. Even if they come out slightly crispy, they will soften overnight. I do roll mine inbetween two sheets of waxed paper. This minimizes the amount of extra added flour that you'd have to add otherwise. Follow the same baking instructions as your usual recipe. I bake mine until lightly golden around the edges. I hope this helps!
Enjoy!
SC

4 sticks butter or margarine, room temp.
2 cups sugar
2 eggs
2 tsp. vanilla
4 tsp. baking powder
6 cups flour

Cream butter and sugar together, add vanilla and eggs, mix well. Mix flour and Baking powder well, and add
to the other ingredients. No chilling necessary. Roll out dough on lightly floured surface.
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Soft Sugar Cookies (rolled)

This recipe has been doubled from original recipe, it was small. This makes about 75 good size cookies. They will be soft and melt in your mouth.

2 cups butter
2 cups sugar
6 eggs
3 tsp. vanilla
7 cups flour
4 tsp. baking powder
1 tsp. salt

Cream butter and sugar until light and fluffy. Beat in eggs and vanilla. Mix flour, baking powder, salt. Gradually blend into mixture. Chill dough overnight.

Roll out a small portion of dough on a lightly floured surface. When finished with that take the scraps and put some fresh dough with it, they just seem to turn out best this way. The cookies are rolled out fairly thick.

Bake at 375 only until cookie puffs up. About 6 minutes. Cool and frost with a butter cream frosting and I add different types of sprinkles. May also brush egg white on and put colored sugar on and then bake.

BTW, I have doubled this recipe as well, made about 150 cookies, I bake them for my kids class parties and have enough to give some away as well. These are work, so last time, I baked them one day and decorated the following day. That was much better, instead of being in the kitchen a full day.