Preheat oven to 350 degrees F. Line cookie sheet with parchment paper.
In a mixing bowl beat sugar, vanilla, lemon peel and 6 tablespoons of butter with an electric mixer until well blended. Add eggs one at a time, beating well after each addition. Continue to beat for 1 minute.
Stir in flour and baking powder (will be a soft, sticky dough). Chill the dough for a bit & use a cookie press. Pipe 2-inch diameter rings onto the prepared cookie sheet.
With moistened fingertips, press ends of each ring together to form a smooth ring.
Bake about 20 minutes or until golden brown.
To make icing: Melt 1 tablespoon of butter over low heat. Add sugar, water, lemon juice and vanilla and whisk until sugar melts and mixture is heated through. Thin with more water if icing is too thick to brush.
Remove cookies from oven and immediately brush warm icing over hot cookies. Cool iced cookies on sheet for 2 minutes. Transfer to a rack and cool completely.