In large bowl, beat butter, 1/3 cup powdered sugar and the vanilla with electric mixer on medium speed until well blended. Stir in flour until dough forms. Cover; refrigerate 30 minutes for easier handling.
Heat oven to 350°F Shape dough into 1-inch balls. On ungreased cookie sheets, place balls 2 inches apart. Press thumb into center of each ball to make indentation.
Bake 8 to 10 minutes or until light golden brown. Immediately remove from cookie sheets to cooling racks. Cool completely, about 30 minutes.
Fill cookies with lemon curd. Sprinkle powdered sugar over cookies.