Spoiler warning for those not caught up through “Hildebrandt’s Starling."

In “Hildebrandt’s Starling,” which marks the halfway point of TNT’s gorgeously gothic limited series The Alienist, Dr. Laszlo Kreizler visits one of his old Harvard professors in the hopes of finding a way to see his case with new eyes. Has he become too dogged in the pursuit of one theory? Is he, as Sara later accuses him, becoming intractable? His professor reminds him of one of his earliest lessons, to “look at your bird.” The point of the exercise was to force the young Kreizler to see beyond the conclusion and instead focus on the meat of the process: investigation and analysis.

And so, halfway through its own story, The Alienist is asking us to look at our bird again. By the show’s third episode, “Silver Smile,” we had a good sense of who the serial killer at the center of the mystery might be. Through the work of Kreizler’s informal task force along with scenes only we viewers were privy to, it seemed clear that Willem Van Bergen — with his silvery smile thanks to mercury chloride used for the treatment of syphilis — was the killer. Armed with that knowledge (seemingly), the show cleverly lessened one possible tension (the “whodunnit?”) in favor of a more potent one: how will he be caught?

There's nothing simple about the case itself, but savvy TV viewers will be fairly used to the narrative beats of pursuing a psychotic murderer. Then “Hildebrandt’s Starling” pulled an interesting swap that doesn't exactly count as a twist, but rather, a new psychological question. Most viewers could have guessed that when Roosevelt went to knock on Van Bergen’s door it would not in fact be Van Bergen who answered. It’s a gloriously frustrating thing to see our heroes several steps behind the murderer, which raises our anxiety about when and how they might make up that space. But more intriguingly, Kreizler tells Roosevelt that he doesn’t believe Van Bergen is the murderer. Despite his time spent leering at children and drugging boy prostitutes, he seems to mostly want to spoil them, giving them candy and milk baths. Is he capable of murder? Kreizler doesn’t think so, insisting that the man they are looking for is replicating his own childhood poverty by seeking out immigrant boys. And yet, a creepy scene towards the end of the episode between Van Bergen and his mother seems to back up Sara’s hypothesis that the killer has a strong woman running his life.

Now The Alienist raises an even more fascinating question: Is the Van Bergen “reveal” nothing more than a bait and switch? Are his actions just red herrings as the show investigates an array of different sexual appetites? Kreizler’s trip to Boston to look at his bird again, as it were, revealed that he doesn’t know as much as he thinks — but that’s uplifting in many ways. He’s not alone in this investigation, and a fresh perspective and a willingness to explore other ideas could be just what the team needs to catch the real killer, whomever he may be.

It’s a lesson the show wants us to learn as well, because what makes The Alienist so compelling is not finding out who did these crimes, but how that person will be caught. If you strip away the gothic aesthetic and the allure of the film stars at its center, or take away the intricately detailed and costumed setting and deep character work, then indeed, the story boils down to a simple procedural. But on that ordinary framework, The Alienist has built up an engrossing world by folding all of these other stylistic elements on top of it. And indeed, the investigation itself (which was, for its time, radical and often grotesque) is part of that ghoulish charm. It’s like Penny Dreadful meets a network procedural, and the results have been increasingly satisfying.

Yes, The Alienist’s dialogue can be clunky or overly explanatory, and sometimes it can be a little slow in its digressions. But scenes can be wondrously electric in the smallest moments, especially when Kreizler and Sara are involved. Even Brian Geraghty’s Roosevelt finally had cause to show us a little Rough Rider spirit in this latest episode. What has stood out the most about the series though, which has been steadily growing on me since I reviewed its first two episodes, is how immersive it is. It’s beguiling and a little repulsive all at once (no show may have a more gleeful foley artist right now), but it draws you in fully to its finely-crafted world. It doesn’t need incomprehensible twists and turns and shocking reveals like so many current murder mysteries on TV. Instead, it makes its case by working its case, and sticking with it. Look at your bird again. And again. And again.

The Alienist airs Monday nights on TNT.