Preheat oven to 375ºF.
Combine flour, baking powder and salt in small bowl; set aside.
Beat butter and sugar at medium speed until light and fluffy.
Beat in egg, 1 tbsp. lemon peel and vanilla until well blended.
Gradually beat in flour mixture on low speed until blended.
Drop dough by level ¼ cupfuls onto ungreased cookie sheets, spacing 3” apart.
Flatten dough until 3” in diameter with bottom of glass that has been dipped in additional sugar.
Bake 12 to 14 minutes or until cookies are just set and edges are golden brown.
Cool on cookie sheets 2 minutes; transfer to wire racks.
Cool completely.
Combine powdered sugar, lemon juice and remaining 1 tbsp lemon peel in small bowl; drizzle mixture over cookies.
Let stand until icing is set. (Makes about 1 dozen (4-inch) cookies.