To make Italian lemon cookies from scratch, cream 1/2 cup sugar and 1/4 cup shortening, and then beat the mixture with 3 eggs and 1 1/2 teaspoons of lemon extract. Complete the dough by adding 2 cups of flour, 1 1/2 teaspoons of baking powder and 1/8 teaspoon of salt. Drop small pieces of dough on a greased cookie sheet and bake them in a preheated 350-degree oven until they've lightly browned.
Alternatively, beat together 1/2 cup of sugar, 3/4 stick of butter, 2 teaspoons of vanilla extract and 1 teaspoon of grated lemon peel until they're well combined. Add 3 large eggs one at a time and beat the dough well after each addition. After beating the mixture for a full minute, mix 2 cups of flour and 2 teaspoons of baking power separately, and add them to the sugar mixture and combine. The dough should be soft and sticky.
Prepare the icing by heating 1 tablespoon of butter, 3 cups of sifted powdered sugar, 2 tablespoons of water, 2 tablespoons of lemon juice and 1 teaspoon of vanilla extract until the butter melts and the sugar dissolves.
Use a pastry bag to pipe rings of dough onto greased cookie sheets, and smooth the ends together with a wet finger. Bake the cookies for 20 minutes or until golden brown. Remove them from the oven, and brush on icing before the cookies cool.