Look no further than “Moonlight,” “Angel,” “Forever Knight” and seemingly every vampire show ever bloody well made. At least John Amsterdam, the 300-and-some-year-old protagonist of FOX’s midseason series “New Amsterdam,” doesn’t count himself among the undead.

Amsterdam is a different kind of immortal — a regular guy given eternal life in 1642 by a Native-American girl whose own life he saved.

Also, credit Amsterdam for not becoming a homicide detective until the 21st century. Through flashbacks, we know that John, who doesn’t grow old, but changes jobs and identities every 10 years or so, has worked as a lawyer, furniture maker, carriage driver and soldier before giving the policeman’s badge a try.

Unfortunately, a majority of the show takes place in present day, meaning “New Amsterdam” — airing Mondays at 9 p.m. — is one of those high-concept fantasy series hung on the frame of a low-concept procedural.

In 2008, Amsterdam (the destined-to-be-misspelled Nikolaj Coster-Waldau) and his partner Eva (the almost-as-tricky Zuleikha Robinson) spend their days solving New York City murders. Amsterdam’s pretty darn good at his job, considering he’s studied the human condition for a few centuries and knows the Big Apple better than the rest of its citizens (some of whom have only lived there for a measly half-century).

Their cases are boring “CSI” retreads, and the killer can usually be fingered by the home viewer long before Amsterdam arrives at the solution.

Still, if you can look past the rote detective work, there are some things at play that make “New Amsterdam” an interesting addition to the immortal-crime-fighter genre. As is the norm with the gift of immortality, Amsterdam’s comes with a catch. If he can locate his true love and their “souls are wed,” he will turn mortal once more. It’s a loophole Amsterdam hopes to exploit because he feels only death can give time value. (“To die is what makes life worth living,” he says.) Plus, he’s kind of a romantic, having racked up quite a few dalliances (and marriages and kids) over the years looking for his soul mate.

Where “New Amsterdam”’s writers really prove their smarts is in making that soul mate an actual, definable person — not some vague, off-camera presence.

In the show’s first episode, Amsterdam suffers a heart attack at the subway station and assumes his true love must have been nearby. He becomes obsessed with tracking down the woman who temporarily felled him and grows to believe that she’s Sara Dillane (Alexie Gilmore), a local doctor who’s attractive, separated from her husband and intrigued by Amsterdam’s strange hospital test results.

Coster-Waldau infuses Amsterdam with a heaping of quirky charm. He’s borderline goofy in the way he aggressively courts Sara and casually remarks about things he saw 200 years ago (knowing nobody’s going to believe him). He shares his secret with his senior-citizen-age bartender son and cleverly names his dogs by how many pets have come before. (His new pooch goes by “36.”) Immortal crime fighters are often morose, broody individuals, but not John. He smiles a lot and actually seems to have enjoyed his long, eclectic life, which strangely puts his character at odds with the grisly murders the show dumps on him (and us) each week. It’s almost like “New Amsterdam” is two different series — one that you’ve seen a million times before, and one that you’d like to see a little more of.

There’s certainly evidence that it could transcend its procedural trappings and evolve into a drama worth watching, if only the writers would lay off the Joe Friday stuff once in a while. Of course, FOX will also need to give the show time to find its footing, something that network isn’t always wont to do.

“New Amsterdam” won’t have the lifespan of the character it’s named for, but a full second season wouldn’t be such a terrible thing.

Remote control in hand, Bob Taylor monitors the TV landscape from his couch and diligently reports his findings to you. If you have a question or comment for Bob, e-mail him at bobtaylor52@yahoo.com. If you want your e-mail to be considered for publication, please include your first name and the town you live in. You can find Bob on the web and read past installments of “Taylor on TV” at www.robertbriantaylor.com.