À la Nivernaise means “glazed.” Typically, the food item being glazed is a vegetable, and typically, the glaze is made from butter and sugar, though butter and a citrus juice, or butter and wine, may also be used instead of sugar to make the glaze.
“Carottes à la nivernaise” may be just glazed carrots on their own, with a glaze made from butter and sugar. Classically, these “Carottes à la nivernaise” were served with roasted or braised meats, particularly braised duck, or pieces of other wild fowl.
“Petits pois à la nivernaise” is peas with carrots and onions in a butter and sugar glaze.
“Champignons à la nivernaise” is mushrooms in a glaze of butter and lemon juice (with crème fraîche and some white wine added.)
If a menu refers to a meat item being “à la nivernaise”, it frequently means accompanied by a garnish of carrots and glazed onions.
The phrase refers to Nevers, in the Bourgogne region of France. Nevers became famous as a production centre for tin-glazed earthenware after two brothers named Corrado introduced the technique to Nevers from Italy in 1565.