In medium sized bowl, combine flour, baking powder, and salt in bowl and set aside. In large bowl, rub lemon zest into sugar until moist and fragrant. Add butter to the lemon sugar and beat until light and fluffy - 3-5 minutes. Add egg and vanilla, mixing until smooth. Add flour mixture, mixing until just incorporated. Fold in cranberries by hand. Cover and chill for least 30 minutes, Longer is better.
Preheat oven to 350ยบ. Gently form dough into balls and bake for 13-15 minutes on parchment lined cookie sheets. Let cookies cool slightly before moving them to rack to cool completely.
To make glaze: mix powdered sugar and lemon juice together, and drizzle over fully-cooled cookies.