MOSCOW — It’s akin to Turkey at Thanksgiving: On New Year’s in Russia, revelers traditionally consume lashings of Olivier salad. 

It was introduced to the then-Russian Empire in 1860 by French chef Lucien Olivier, but these days everyone has a slightly different recipe. It’s so popular that the cost of its staple ingredients — which usually include sausage, potatoes and dollops of mayonnaise — have their own price index that’s tracked by the media.

With soaring inflation and the…