Preheat oven to 325 degrees F.
Dice the butter and put into a food processor with the flour, and sugar. Pulse in short intervals until the mixture is crumbly and resembles coarse bread crumbs. Add the cold egg yolk, salt and water to the mixture, this will make a pastry dough. Place the dough onto a floured surface and form into a ball. Wrap in plastic and place in the refrigerator until cold.
When the dough is cold, place on a floured surface and roll out to cover the bottom of a 13 by 9-inch pan. Bake for 20 minutes.
Whisk eggs together and set aside.
In a separate bowl mix the sugar, flour and baking powder together. Add the lemon zest and juice. Mix in the eggs until well combined. Pour the mixture over the par baked crust.
Place in the oven and bake for 30 minutes until the center has set firmly. Remove from the oven and allow it to cool. Cut into bars.
In a large bowl, mix all ingredients together and blend with a hand mixer on low until creamy. Pipe frosting onto lemon bars.
If you don't have a food processor you can use a pastry cutter, a fork or your hands. If using your hands be careful not to over mix or allow your hands to warm the butter.