With an electric mixer, beat together butter and sugar until light and fluffy. Mix in poppyseeds and lemon zest. Add flour and salt and mix well to make a stiff dough.
Divide dough in half and roll each piece in wax paper to make a cylinder about 2 inches in diameter and 6 inches long. Refrigerate dough until firm, at least 4 hours.
Meanwhile, preheat oven to 350°F and oil baking sheets or line them with parchment paper.
Slice dough into rounds about 1/4 inch thick. Arrange about 1 inch apart on cookie sheets. Bake 12 minutes or until edges are browned. Let cookies cool on baking sheet for a few seconds and then remove to a wire rack and let cool completely.