Bring a large pot of salted water to a boil. Prepare an ice bath.
Cook the green beans until crisp-tender, about 3 minutes. Remove the green beans from the pot and plunge them into the ice bath to stop the cooking process. Drain and set aside.
Heat a 10-inch skillet over medium heat. Add the butter and oil. When the butter begins to foam, add the garlic and cook until golden brown, about 3 minutes. Stir in the anchovy paste, and then add the wine. Bring to a simmer, stirring, about 2 minutes. Add the green beans and toss to coat. Cook 2 minutes more, then add 1/2 teaspoon salt and remove from the heat. Serve immediately.
A viewer or guest of the show, who may not be a professional cook, provided this recipe. It has not been tested for home use.