Grease a cookie sheet with margarine or butter and set aside.
Beat 1/ 2 c. butter and 3 tbsp. sugar to a light, frothy texture. Stir in flour as lightly as possible until mixture is like fine bread crumbs.
Turn mixture onto a floured surface and knead gently until it forms a smooth dough.
Form dough into a circle 6 inches in diameter and ¥-inch thick and transfer it to the cookie sheet. Prick surface of dough lightly with a fork. Refrigerate dough for 20 minutes.
Preheat the oven to 350°F. Bake shortbread for 30 minutes. Then turn the oven down to 300°F and bake for 30 to 40 more minutes, until it is crisp and lightly browned.
Remove the cookie sheet from the oven. With a sharp knife, cut shortbread into 8 triangles. Let triangles cool slightly on the cookie sheet, then transfer to a wire rack to cool completely.
Serve shortbread immediately or store in an airtight container.