Big Maggie's big list of fabulous monster men:
Alucard (Hellsing)
Asgore (Undertale)
The Babadook (The Babadook)
The Beast (Beauty and the Beast, 1994)
Bowser (Mario)
Crow Mauler (Fear & Hunger)
Deadpool (Obnoxious & Debatable)
Gannondorf/Gannon (The Legend of Zelda)
Geralt of Rivia (The Witcher)
Guy Fieri (real?)
Hamlet's dad who is also named Hamlet (Hamlet)
Mephistopheles (Faust)
Morgott and Mogh (Elden Ring)
Nightcrawler (X-Men franchise)
Nosferatu (as played by Klaus Kinski in the 1979 Werner Herzog remake)
Nosferatu (as played by Max Schreck in the 1919 film by F.W. Murnau)
Orgrim Doomhammer (World of Warcraft, namesake of Orgrimmar)
Papyrus & Sans (Undertale)
Polyphemus (The Odyssey)
Professor Lupin (Harry Potter)
Pyramid Head (Silent Hill)
Shrek (Shrek, 2001)
Tetsuo Shima (Akira)
Yoda (Star Wars)
What makes a monster man?
Not having a typical, sexy human-man body is a good start. Being a literal monster from the bestiary is best. Characters capable of transforming into gruesome things (e.g. Alucard) and unable to die a normal death are monsters. Lycanthropes are OK. Corruption of a normal guy by evil (e.g. Crow Mauler) so that it grants him supernatural qualities counts. Potentially acquiring or being an infectious nightmare contagion counts (e.g. Pyramid Head, Tetsuo Shima). Ghosts and spirits count if they can interact with the living & are not too silly (e.g. Hamlet's Dad = OK, Slimer = Not.) Also they need to be male, obviously.
What isn't a monster man?
A man who enjoys all strength of being a monster but none of the disfigurements is not a monster but a godlet. Edward Cullen and his many genre lookalikes, Miquella the Kind, Superman, Hercules, etc. have beautiful human forms and their limitations are more++ than compensated with benefits. Monster men can't be Greek Gods or lesser godlets of certain pantheons. Messianic figures like Jesus & Harry Potter don't count, because their supernatural qualities are from grace and divine favor. A monster man is at most breaking even in benefits : drawbacks with regards to his monstrousness. IMO men trapped in robots or physically compromised by machines (e.g. Mettaton, Wolverine) are not monster men, they're mechanically enhanced men. Regular men of race with anger problems and violent tendencies don't count (e.g. Heathcliff is not a monster man, he's an angry drunk gyppo. Dr. Hyde is not a monster man, he's a coke fiend.)
Are they sexy?
You tell me.