As a partner at Employees Only in the West Village, Billy Gilroy made his name by reviving Prohibition-era cocktail culture, a bar trope that shows no signs of waning. At East Side Social Club, his latest restaurant in midtown, he’s attempting another campy resurrection, this time of an Italian-American dinner club circa 1950, the kind of place where you might start with an old-fashioned and end with a grasshopper (and you should: The drinks are as good as Gilroy’s pedigree would suggest). Thanks to its midtown location and convincing decor (red checkered tablecloths, tacky Mediterranean murals), it’s unclear whether customers will pick up on the irony of the place: It’s easy to imagine unsuspecting walk-ins making a beeline for the door, fearing either subpar meatballs or the wrath of a resident wiseguy. As far as food and service are concerned, they have nothing to worry about. The kitchen, run by Billy’s son Devon, presents a sophisticated spin on red-sauce fare. However, some prices are so high you may end up feeling shaken down. An $18 appetizer of supple grilled octopus came with one midsize tentacle and a few extra pieces on a bed of fingerling potatoes dressed in a mustard-seed vinaigrette. Tender fried sweetbreads blended agreeably with fragrant orange and fennel, though $17 seemed steep for the average-size serving. Strands of spicy-marinara-coated spaghetti, meanwhile, cradled succulent lobster that retained its sweet sea taste, and a special 40-ounce rib-eye steak was buttery soft, but the $56 charge was harder to stomach. Thoughtful desserts are worth a try—house-made biscotti with saffron gelato and olive oil—though cannoli fell short of perfection due to pastry that tasted of stale oil. As we watched a real-life goombah manhandle his date at a nearby table, it became even clearer how important context is to a restaurant: Downtown, most everyone would be in on the fun, but up on 51st Street, the humor is largely lost.