Preheat oven to 350 degrees F. Line two cookie sheets parchment paper; set aside.
Beat the butter and sugar in a large bowl using an electric mixer about 2 minutes or until light and fluffy. Add the egg and vanilla and beat until well blended.
Combine the flour, baking powder and salt in a medium bowl. Add half of flour mixture to the butter mixture, beating until just combined. Add the milk. Beat about 10 seconds. Beat in the remaining flour mixture until just combined.
Stir in orange and lemon peel until combined
Using a cookie scoop, drop dough onto prepared cookie sheets.
Bake 8 to 10 minutes or until set and the bottoms have browned. Transfer the cookies to a wire rack; cool completely.
For the orange glaze, combine the butter and orange juice in a small bowl. Add powdered sugar and beat until smooth. Spoon over cookies.