Cream butter until smooth, add sugar and egg, and beat until smooth and fluffy.
Sift in flour and blend thoroughly Stir in nuts until well distributed.
Shape dough in small balls and flatten out with a flat-bottomed glass covered with a clean, slightly dampened cloth, to about 1/8-inch thickness on a greased baking sheet.
They should be at least 1 inch apart when flattened.
Bake in a moderate oven (375° F.) for 12 minutes, or until nicely browned.
Cool on pan 2 to 3 minutes; transfer to cake rack.