Twisted Minds

I've heard that a witch hunter is holding up in Diamond City. I should see what all the fuzz is about.

Detailed Walkthrough
Brooke can be found at the Dugout Inn, located in Diamond City. When trying to speak with her, the Sole Survivor will have to wait for her and Vadim Bobrov to finish arguing first. After that, Brooke will question the Sole Survivor's occult beliefs and ask them to go with her to Dunwich Borers.

Upon reaching the end of section 4, Brooke will ask the Sole Survivor to donate some blood for a ritual to conjure forth a dark artifact. Upon their agreement, Brooke will bring forth the artifact and then ask to go to Pickman's Gallery. The other blade in the water can also be retrieved at this time.

After exploring Pickman's Gallery, finding Pickman, and saving him from Slab's gang, he will offer his usual reward and then start another conversation with Brooke. After this conversation, the Sole Survivor can re-enter the gallery to both claim their reward and to continue learning about Rotihar and Ug from Pickman's occult research, which he shares with the Sole Survivor and Brooke.

Brooke will ask to go to the Coastal Cottage settlement at this point. When near the settlement, the Sole Survivor will have to kill any raiders and other randomly encountered enemies nearby before they can reach the quest update point and have a peaceful conversation with Brooke to continue the quest.

Brooke will tell the player that they must swim to Zanoth's lair. Having Aqua Boy/Girl is good, but not necessary because it's a very short swim to the cell transition. Shortly after entering the Zanoth's lair, he and a gen 1 synth will appear. Zanoth will immediately kill the synth and then stand in place, allowing the Sole Survivor to converse with him.

The Sole Survivor can choose to either kill Zanoth (even though he is said to be immortal) or to betray Brooke and serve Zanoth instead. Betraying Brooke grants the Sole Survivor the Zanoth's Blessing perk, which grants a 10% bonus to damage and XP at night and also completes the quest. Siding with Brooke eventually leads to her becoming a free settler at Coastal Cottage. Rotihar's Blade is awarded either way.

Both Brooke and Zanoth can be conversed with after betraying Brooke. Brooke will be very unhappy and explain that she is trapped by a spell in Zanoth's lair for the rest of her life, which is eternity because she is immortal. Zanoth has options to give flavor text about being sexually pleased by Zanoth, and he may offer a radiant quest to kill a demon.