Cream the sugar and the butter in the bowl of an electric mixer for about five minutes, until very fluffy. Then beat in the eggs and vanilla. Scrape down the sides of the bowl with a rubber spatula halfway through the beating.
In a second bowl, combine flour, salt, and zest. Add to sugar-butter mixture and beat with a paddle attachment slowly until blended, scraping down the sides of the bowl now and then. When the mixture is smooth, roll it into a fat cylinder, wrap with plastic wrap, and refrigerate for at least two hours.
When ready to bake, preheat the oven to 350 degrees.
Roll the dough out to about the thickness of two stacked quarters. Cut into circles about 3-4 inches in diameter. Put about two teaspoons of preserves into the center.
Fold the dough circles up into triangles, pinching as small a seam as possible to close up the preserves. Put the hamentaschen on greased cookie sheets and into the center of the preheated 350 degree oven for about 25 minutes, till lightly browned. Allow to cool before serving.