Cajoling a Cudgel

 is an unmarked quest in Fallout: New Vegas.

Quick walkthrough
Begin with locating Luke's find, a key which unlocks the Sealed Sewers. You can find it on the bodies of two dead Prospectors, 'Sweet' Jill (in the East Central Sewers) or 'Blind' Luke (in the Central Sewers).

Once obtained, you can enter the Sealed Sewers and check the Prospector's corpse, on which you will find a unique weapon, The Humble Cudgel.