Back in 1990, the playwright David Henry Hwang protested a decision by the British theatrical producer Cameron Mackintosh to bring Jonathan Pryce, the widely admired British star of his hit London musical “Miss Saigon,” to Broadway. Pryce played a weirdly nonspecific Asian character called The Engineer and makeup was employed to alter Pryce’s Caucasian features. Hwang, who had already scored a hit with “M. Butterfly,” argued this casting was unacceptable. Period. A huge contretemps, a fight I well remember, ensued. On one side was racial authenticity, or the lack thereof in this case, and the denial of opportunity to Asian-American actors, historically confined to minor roles on Broadway, if they got any role at all. Daniel Dae Kim, Kevin Del Aguila, Marinda Anderson and Francis Jue in “Yellow Face” on Broadway. (Joan Marcus)   On the other was the argument that this was clearly a slippery slope. Did this mean actors always had to be gay to play a gay character? Jewish to play a Jewish hero? What about mixed-race performers? Was it about how people appeared or identified, or about the race of their parents? And at an audition, how could you even know for sure who was what? Federal laws intended to prevent racial discrimination made it illegal to ask. At the time, most outsiders and even liberal theater critics sided with the producers. My, how the world has changed. And, in this matter, mostly for the better. Francis Jue, Marinda Anderson, Kevin Del Aguila, Daniel Dae Kim, Ryan Eggold and Shannon Tyo in “Yellow Face” on Broadway. (Joan Marcus)   Hwang’s semiautobiographical play, “Yellow Face,” new on Broadway at the Roundabout Theatre, actually premiered some 17 years ago Off-Broadway, also under the solid direction of Leigh Silverman. Naming real names, most of whom still are very much around, the 90-minute show looks back at this 34-year-old affair, focusing on the discomfort the author felt at being caught between fighting what he saw as oblivious racism and being perceived as standing on the wrong side of artistic freedom. The vexing situation was exacerbated by the producer’s declaration that without Pryce’s star power and skills he would choose to cancel the show — thus Hwang quickly found himself in the position of potentially putting the many Asian-American actors who had been cast in this large Broadway company out of work. Francis Jue and Daniel Dae Kim in “Yellow Face” on Broadway. (Joan Marcus)   On some levels, “Yellow Face” is inside-baseball Broadway, most interesting to those who follow issues that tend to engage only a subset of highly educated Americans and/or those who work in the cultural fields. That said, we quickly forget that “Miss Saigon” was a populist phenomenon back in the day and made front page news. And what makes this an enjoyable play, and different from most of the other dramas built around racial identity, is that “Yellow Face” is (mostly) a comedy and Hwang, who is amusingly played in the show by the witty actor Daniel Dae Kim (“Lost”), is willing to poke fun at himself. Weird as it may sound, “Yellow Face” is a good time in the company of smart, self-aware people, critical thinkers willing to ponder the lessons and the follies of the past. Ryan Eggold, Marinda Anderson, Daniel Dae Kim and Kevin Del Aguila in “Yellow Face” on Broadway. (Joan Marcus) Here’s the rub: Hwang was himself working on a play when the “Miss Saigon” business hit and he, too, needed to find an Asian-American actor shortly afterward.  He thinks he has one, but then he’s not so sure. What if the guy (here dryly played by Ryan Eggold) really is white? What even is a white guy, anyway? Or someone of Asian descent? Doesn’t “Asian” come from the name of a continent that contains myriad identities, an absurdly reductionist term in the first place? A blend of fact and fiction, “Yellow Face” is an admirably self-aware work and instead of simply ignoring the baked-in contradictions of its central dilemma, it explores its limits. Plus, there is an additional rub. Hwang is the son of the Shanghai-born Henry Yuan Hwang (played with palpable joy by Francis Jue), the founder of the Far East National Bank, the first federally chartered Chinese-American bank. The elder Hwang, a registered Republican, was hugely successful in his adopted home and he drew his playwright son into the bank, even as it attracted investigatory attention for its ties to politicians and to China itself. Daniel Dae Kim and Ryan Eggold in “Yellow Face” on Broadway. (Joan Marcus) “Yellow Face” notes that even as the son built a creative career by focusing on the U.S. and European habit of either fetishizing or feminizing Asian nations, his own immigrant father was so patriotic that he even put “I Love USA” on the frame of his license plate as he made his stateside fortune. Did the U.S. treat either of these two remarkable men fairly? Vice-versa? That’s complicated, like everything explored in “Yellow Face.”