Maria. I went through all my Sesame Street library books and I found this recipe in volume 1. It also has the Princess and the pea story, so I'm pretty sure it's the recipe you are looking for. It's a basic cookie dough you can add whatever you want to it. This is the recipe exactly as it appears in the book. It doesn't say how to actually bake the cookies.
Butter or margarine (soft, but not melted)
Sugar
2 eggs
Vanilla
All-purpose flour
Baking Powder
Salt
1.Put 3/4 cup of butter or margarine (that's a stick and a half) into your mixing bowl.
2.Measure 1 cup of sugar.
3.Pour sugar over butter.
4.With a fork, squash butter and sugar together until they are blended.
5.Crack shells of two eggs and pour eggs over mixture in bowl.
6.Measure one teaspoon vanilla and pour over the mixture.
7.With fork, blend everything in the bowl together.
8.Measure 2 1/2 cups of all-purpose flour and pour over mixture in bowl.
9.Measure one teaspoon baking powder and sprinkle over flour.
10.Measure one teaspoon salt and sprinkle over flour and baking powder.
11.Mix everything together either with the fork or with your hands.
12.Put dough in icebox to chill (at least one hour).
I hope this is helpful.