Sift the dry ingredients together into a bowl.

In another bowl, beat the butter until it is light in color, gradually adding the sugar. Add the egg and vanilla and continue beating the mixture until it is very light and fluffy. Add half the flour beating it in; then add the rest with your hands to form a stiff dough. Refrigerate the dough for one hour before rolling it out to harden it a bit.

While the dough is cooling in the refrigerator, make the filling: Combine the dates, sugar, and water in a pot. Cook the date and sugar mixture, stirring, over medium heat until it is thick, about five minutes. Remove from the heat and add the nuts and lemon peel. Let it cool before using.

When the dough and filling have cooled, divide the dough in half. Roll each half into an 8" x 10" rectangle. Spread each rectangle with half of the date nut mixture. Roll each rectangle jelly roll fashion and gently press the end edge to seal. Wrap in foil or waxed paper and refrigerate until firm, preferably overnight, before baking.

Preheat the oven to 375°F and lightly grease one or two cookie sheets.

Cut the dough into 1/8 inch thick slices and lay them on the cookie sheets. Bake for 8 to 10 minutes or until they are lightly browned on the bottom but still fairly white on the top. Let the cookies stand for one minute before removing them from the pan to cool on a rack.