Oven: 300 F for cookies; 275 F for large whole shortbread
Cream butter until light. Add sugar gradually, beating until fluffy. Add flour 1/2 cup at a time to a total of 2 cups, mixing well. Turn dough out onto a pastry board floured with the final 1/4 cup flour. Knead in this last 1/4 cup, then divide the dough in two and knead each until all cracks disappear (about 5 minutes). Refrigerate for 15 to 20 minutes.
Roll out each piece to 3/8" thickness. Cut into desired shapes or leave whole and crimp edges and prick surfaces with fork. Bake on ungreased cookie sheet to slightly golden, 25 to 30 minutes for cookies and 30 to 35 minutes for whole shortbread.