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