The Chelsea building occupied by the London-based theater company Punchdrunk for their hit immersive spectacle Sleep No Moreappears to contain multitudes. The show itself unfolds over several floors in the sprawling complex, which is designed to evoke an old haunted hotel (called The McKittrick). Last year the roof was transformed into a bucolic destination called Gallow Green, serving punch, live music, and gourmet bar snacks, and now an entirely new floor in the hotel—previously used for storage—is an enchanting restaurant and jazz club called The Heath.

The highly theatrical restaurant, marvelously designed to resemble an early-20th century train station, serves a modern take on classic American and British fare from Chef R.L. King. There's a Spit Turned Lamb Leg with braised beans, baby carrots, cippolini onions, parsley pesto ($32); a Fisherman’s Pie with halibut, scallops, shrimp, cod, salmon, braised leeks, parsley velouté, and mashers ($30); an appetizer of Bitter Greens with meyer lemon, red onion, pistachios, and cheddar ($13); and share plates including options such as Crispy Pig Crunchies with tartar sauce for $9.

Several cozy rooms off to one side are designed to resemble well-appointed private dining cars, and a stage in the bustling main dining room is home to a swinging jazz band that keeps things lively without drowning out conversation. And in the spirit of Sleep No More, a smattering of eccentric "characters" work the room, chatting up guests as if they've just stepped out of a steampunk time machine. The theatrical element is as immersive as you want it to be—at any point an exotic man or flirtatious woman might approach your table and slip you a hand-written note with your name on it, saying "I can't believe you're here" and asking you to rendezvous at "Platform 1."

Tempting, but you may be too busy sipping cocktails and scarfing Pig Crunchies to make the connection. The cocktails are all $15, expensive but sophisticated, and if you're not hungry you can nurse your drink at the bar, which has a view of the stage. At the press preview last month I tried the Norseman, a bracing concoction made with Eau de Vie de Pomme, Laird’s Bonded Applejack, Cocchi Torino, Nardini Bassano, and Orleans Bitter; also recommended is the smooth and refreshing Hull Executive: cippollini-washed Aalborg (a Danish liqeuer), Hendrick’s Gin, Dolin Dry, and Cocchi Bianco. After a couple of these you may be inclined to meet that stranger over on Platform 1 and see where it goes.

542 West 27th Street // More details here, including online reservations // 212.564.1662

Here's the full menu below.

The Heath Opening Menu