A Melted Hunk of Metal
Despite the burn damage, you recognize this weapon as a Thorn, a legendary weapon capable of severing Guardians from the Light. The Shadows of Yor, followers of an infamous Guardian-killer, are well-known for carrying Thorns. This one is broken, but you think it may be possible to fix it. A reputable (and discreet) gunsmith would know where to start.
Bring the ruined Thorn to Banshee-44 in the Tower.