Lemon Tea Cookies

I love tart lemon desserts. This is a recipe I found on Betty Crocker that looks very good.
Makes 3 dozen Cookies

Cookies
1 cup butter or margarine, softened
1/3 cup powdered sugar
1 teaspoon vanilla
1 2/3 cups flour
1 tablespoon powdered sugar
Filling
2/3 cup granulated sugar
3 teaspoons lemon peel, grated
3 tablespoons lemon juice
1 tablespoon butter or margarine
1 teaspoon cornstarch
1/4 teaspoon salt
1 egg, beaten

In large bowl, Beat butter, 1/3 C powdered sugar, and vanilla with mixer on medium speed until well blended.
Stir in flour until dough forms.
Cover; refrigerate 30 minutes
Heat oven to 350°F Shape dough into 1" balls.
Place balls 2" apart. Press thumb into center of each ball to make indentation.
Bake 8 to 10 minutes or until golden brown.
Remove to cooling racks and cool completely, about 30 minutes.
In 1 qt saucepan, heat all filling ingredients over low heat about 25 minutes, stirring constantly, until smooth and thickened.
Cool about 15 minutes.
Fill each thumbprint with rounded 1/4 tsp filling. Sprinkle 1 T powdered sugar over cookies.