Why isn’t Paul Thomas Anderson’s “Punch-Drunk Love” his cult classic? His 2002 curveball take on the romantic comedy seems like a perfect candidate for midnight-movie showings, Twitter bio quotations, and Threadless T-shirt designs. I’m surprised we don’t see more millennials getting married with the groom in a royal blue suit.

And yet “Punch-Drunk” seems to have been the forgotten PTA film, the ellipsis between his first trilogy of independent films (“Hard Eight,” “Boogie Nights” and “Magnolia”) and his recent trilogy of period films subverting traditional American male archetypes (“There Will Be Blood,” “The Master” and “Inherent Vice.”)

A new Blu-ray of “Punch-Drunk Love” out from the Criterion Collection should hopefully help people rediscover the film, although even that seems a little light on bonus features that go beyond the original DVD release, at least for Criterion. It’s a shame, because it’s a movie that keeps me giddily off-balance in every way.

Anderson daringly, and perfectly, cast Adam Sandler as Barry, a vibrating man-child who mumbles his way through a humdrum existence, until his life is sidelined by a trio of quests. First, he finds a harmonium abandoned on the street and tries to learn to play it. Second, he thinks he’s figured out the loophole in a pudding-cup contest that will allow him to rack up unlimited Frequent Flyer miles. Not that he travels, but the thought of victory is enough to send Barry into a delightful little tap dance in the grocery aisles.

Third, and most important, is his quest to get over his shyness and self-loathing and win the heart of fair maiden Lena (Emily Watson). This quest is complicated by a dragon, in the form of a furniture store salesman and phone sex tycoon played by the late great Philip Seymour Hoffman.

It’s a strange movie, part slapstick comedy and part tender character study, but unabashedly sweet in its heady invocations of the joy and terror of new love. As composer Jon Brion says in an extended interview on the Criterion disc, Anderson wanted it “to feel like a musical, but nobody actually ever breaks out into song.”

The key new features on the disc focus on Brion’s baroque, percussive, unsettling score, which feels like the jumbled thoughts in Barry’s head spilling out onto the soundtrack. Brion explains in the interview that, rather than working on the music after the film was completed, as is standard, he was composing alongside Anderson’s shooting schedule, ideas batting back and forth between them.

In fact, Brion’s score was a key factor in Sandler’s amazing, never-repeated performance — once he heard what the music was going to be like, Brion said, Sandler realized he could dial his performance way down and let the music suggest Barry’s interior life. Given that “dial his performance way down” was not normally in Sandler’s thespian vocabulary, this was essential.

I would have liked to have heard more from Anderson, over a decade later, on where he thinks “Punch-Drunk” fits in with his career. Brion tells the story of how a veteran filmmaker came to visit Anderson and watch a work-in-progress screening, and gently suggested that the elements of the movie weren’t exactly adding up. “I know,” Anderson was said to have responded with a wide grin. “Isn’t it great?”

“And if more people in Hollywood said that,” Brion tells the interviewer, “we might have some fucking movies to watch.”