Step 1 Heat the oven to 325 degrees. In a stand mixer or medium bowl with electric beaters, beat the butter, sugar and salt until creamy, about 2 minutes, being careful not to overmix. Gradually beat in the flour, working in the last one-half cup with your hands if necessary (the dough will be stiff). Divide the dough in half.
Step 2 2a. To make chewy wedge-shaped cookies, butter 2 (8-inch) metal cake pans and line with parchment. Butter the parchment and press each half of the dough into a pan. Smooth the top with the bottom of a buttered measuring cup. Prick the dough with a fork in a decorative concentric circle pattern. Refrigerate the pans, uncovered, for 30 minutes.
Step 32b. To make crispy bar cookies, shape each dough half into a 10-by-4-inch rectangle on a lightly floured board. Run a blunt knife or your fingers along the edges to straighten them (it doesn't have to be perfect). Carefully lift each rectangle onto a buttered baking sheet, lifting both edges with your hands. With a blunt knife, score each one once lengthwise without cutting all the way through. Score crosswise 11 times to make 24 rectangles. Prick each one several times with a fork. Refrigerate the sheets, uncovered, for 30 minutes.
Step 4Bake both the wedge and bar shortbread until lightly brown along the edges, 25 to 30 minutes. Remove and cool for 5 minutes, then slice the shortbread while still warm (if the cookies are allowed to cool before slicing, they will crumble). Unmold the wedge shortbread by running a knife around the edge of the pan to loosen the cookies from the sides. Gently flip the pan over, then slice the shortbread into 12 wedges. Slice the bar cookies all the way through the scored marks before moving to a cooling rack.