During awards season, a handful of performances from the past year become the only ones we talk about, leaving the rest draped in shadow. If there were a Most Valuable Per Minute of Screen Time award, surely Michael Stuhlbarg’s name would be the one on everyone’s lips.

Since his breakthrough lead performance in the Coen brothers’ “A Serious Man” (2009), Mr. Stuhlbarg, a Juilliard graduate who made a name for himself in New York theater, has been cast only in minor roles in movies, albeit by major directors. He’s probably best known to viewers for his recurring TV characters on “Boardwalk Empire” and “Fargo.”

Now Mr. Stuhlbarg, 49, is enjoying a midlife big-screen breakout, effortlessly elevating everything he appears in. He had a standout year in 2017 with supporting performances in three major awards contenders: “Call Me by Your Name,” “The Post” and “The Shape of Water.” But is he getting his due? While some critics’ groups have given him prizes, he wasn’t nominated for a Golden Globe, and it remains to be seen if the Academy of Motion Picture Arts and Sciences will follow suit.

Far from your typical Hollywood leading man, Mr. Stuhlbarg nevertheless is making a strong case for juicier parts as he quietly steals scenes in acclaimed films opposite more decorated performers.