a conterbore

Webster's Dictionary (GCIDE)

1.An enlargement of the upper part of a hole, forming a cavity or depression for receiving the head of a screw or bolt. [1913 Webster]

Note: In the United States a flaring cavity formed by chamfering the edges of a round hole is called a countersink, while a cylindrical flat-bottomed enlargement of the mouth of the hole is usually called a conterbore. [1913 Webster]

2.A drill or cutting tool for countersinking holes. [1913 Webster]