Bring a large pot of lightly salted water to a boil. Add nettles and cook uncovered until softened, 3 to 4 minutes. Drain in a colander and immediately immerse in ice water for several minutes to stop the cooking process. Drain and chop finely.
Mix nettles, eggs, bread crumbs, parsley, Parmigiano Reggiano cheese, and salt together in a bowl until mixture is combined. Dip hands in warm water and shape mixture into small patties.
Heat olive oil in a skillet over medium heat. Fry patties in hot oil, turning halfway, until cooked through and golden brown, about 10 minutes. Drain on paper towels.