Place the hazelnuts in a large (12-inch) saute pan set over medium heat. Cook for 5 to 10 minutes, rolling them around occasionally, until they are heated through. Transfer the nuts to a clean kitchen towel, fold the towel over and roll them around until some of the skins fall off. (Don’t worry if they don’t all fall off.) Roughly chop the hazelnuts and set aside. Wipe out the pan with a kitchen towel.
Meanwhile, fill a large pot with 4 quarts water, add 1 tablespoon salt and bring to a boil. Plunge the string beans into the water and cook for 5 minutes, until just tender. Drain immediately, plunge into a large bowl of ice water and set aside.
When ready to serve, heat the butter and 1 tablespoon olive oil in the large saute pan over medium-high heat. Add the string beans, 2 teaspoons salt and 1 teaspoon pepper and cook for 3 minutes, stirring with tongs, until heated through. Off the heat, stir in the dill and hazelnuts and taste for seasonings. Serve hot.
When cooking with any kind of nuts, I often toast them before adding them to a recipe because it brings out their flavor and crisps them.