Cream the butter and sugar together. Blend in the flour and chopped ginger to form a soft dough. Divide the dough into 3 parts (the dough is buttery enough that you should be able to do this on a smooth UN-floured surface, like the counter), and roll each into a log about 12 inches long and about 2 inches in diameter. Wrap in wax paper and refrigerate, at least overnight, and for as long as 3 days.
When you are ready to bake, preheat the oven to 375 degrees. Slice the dough rolls into slices about 1/2 inch thick, and arrange in orderly rows on ungreased baking sheets. Place a small square of diced ginger on top of each slice, and put into the oven. After the cookies have been in the oven for about 5 minutes, they will be soft enough so that you can press lightly on each piece of ginger, to make it sink into the cookie. Continue baking unitl very lightly browned. Cool on a rack.