Unfortunately, Broken Man reminded me of an important rule with these kinds of pulpy adventure stories: The first book is never as good as what follows. (The first Doc Savage and Destroyer novels are relatively weak sauce when compared to later installments, for example.) Broken Man introduces readers to Mongo's world—his police officer brother Garth, his long and illustrious career in the circus—but it takes a little while to speed up. Sacred Stone comes later in the series, but it covered all the exposition of Mongo's origins in a paragraph or two, whereas Broken Man slowly lays things out. The central mystery, about the return of a presumed-dead architect, proves to be fairly exciting once it starts chugging along, but it takes about half the book to build Mongo into the suave, disaffected character who pops to life on the first page of Sacred Stone. As in the later books, Chesbro manages in Broken Man to meld supernatural elements with realism, and he does seem to understand Mongo's character thoroughly on the first outing, demonstrating a vulnerability in Mongo that a lot of pulp authors wouldn't be willing to demonstrate in their protagonists.
If you like mysteries, paranormal adventure, or flawed heroes, I thoroughly recommend Chesbro's Mongo series. I just can't recommend Shadow of a Broken Man to you unless you're a completist. I expect that if the Dinklage-led Mongo series ever gets off the ground, they'll jump into the character of Mongo fully-formed and skip all the introductory hoo-ha that Chesbro goes through here. That will be a wise decision.