If you want to get away — I mean really, really away — from concerns of the day, here is “Natasha, Pierre and the Great Comet of 1812.” It’s a massive, luscious, romantic escape into decadent 19th century Moscow by way of Broadway’s Imperial Theatre.

Plush red velvet hugs the walls of the unrecognizably transformed theater (designed by Mimi Lien), now lit with enormous star-burst chandeliers. Curvy brass banisters help guide characters and musicians in preposterously extravagant period and hot-pants modern costumes (by Paloma Young) down aisles, onto cocktail tables and around audiences seated on the stage. Vodka is for sale and, if you’re lucky, surprisingly good pierogi may be tossed your way.

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A splashy gimmick? Sure, but a big, stylish, enjoyable one. Meaningless, yes basically, but with storytelling sustenance alongside the environmental trappings we know as immersive theater. A multifaceted talent named Dave Malloy wrote and composed this seriously beautiful lark of an oddball musical from a brief section of “War and Peace.” The show began four years ago at Arts Nova, the off-Broadway creative incubator, then as now directed by the spectacle-wizard Rachel Chavkin, and has returned in pop-up tents around the city.

On Broadway now with many of its original actors, the production includes the Broadway debut of Josh Groban — in a fat suit — as its thoroughly unlikely and deeply moving headliner from mainstream pop. He plays Pierre, a melancholy mope of an aristocrat and intellectual who observes other people’s vibrant lives with both vanity and self-loathing. No star turn, this is a passionate, subtle portrayal full of both heart and creamy, expressive singing.

Malloy introduces his plot and many characters in an amusing cumulative song — think “The Twelve Days of Christmas” but by Tolstoy. We meet the young Natasha (played with lovely, slightly boring innocence by Denée Benton), betrothed to Andrey, the wealthy absent soldier, but besotted with the dashing Anatole — portrayed by Lucas Steele with irrepressible rock-star vanity and the hair of a platinum woodpecker.

Other standouts in the large, daring, excellent cast include Grace McLean as Natasha’s controlling, shrewd godmother, Brittain Ashford as Natasha’s concerned cousin and Gelsey Bell as Andrey’s repressed sister.

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Malloy adapts the novel’s prose into melodic recitatives — mostly conversational arias, duets and trios that hover in high vocal registers over steady rhythms of rock and Russian folk dance. Inextricable from the music and story are the overwhelming sets and costumes — sensory overload with little on its mind except offbeat entertainment.