Brood Mother - Borderlands 3 Farming Guides
Location: The Pyre of Stars on Nekrotafeyo
Part of: Crew Challenge
Drops: Devoted (Maliwan SMG), Baby Maker ++ (Tediore Pistol) and Scourge (Torgue RPG)
Brood Mother can be found in The Pyre of Stars which is a zone on Nekrotafeyo, the final planet you traverse in the game. In order to reach the Brood Mother you'll need to run all the way around The Pyre of Stars in one giant circle until you find yourself at the end of the zone (which is near the entrance) where you'll find the Brood Mother Crew Challenge. It's a pit of a pita to reach her and can probably be made easier if you have a low level RPG to propel yourself up the cliff face by the entrance.
Note: The Brood Mother isn't a 100% chance to spawn despite being a Crew Challenge. If you come to this location and she doesn't spawn for you just quit to Main Menu and try again.
As far as loot goes, Devoted (Maliwan SMG), Baby Maker ++ (Tediore Pistol) and Scourge (Torgue RPG) are all on the Brood Mother's dedicated drops loot list. None of these items are unique to Brood Mother and can be found elsewhere in the world easily as well.