Grilled Rib Eyes With Mushrooms And Fish Sauce

Name: Grilled Rib Eyes With Mushrooms And Fish Sauce
Ingredients: 2 tablespoons unsalted butter; 2 tablespoons extra-virgin olive oil, plus more for brushing; 2 large shallots, thinly sliced; 2 pounds mixed mushrooms, such as cremini, oyster and shiitake, stemmed and thinly sliced; 2 to 3 tablespoons Asian fish sauce; Pinch of cayenne pepper; 2 tablespoons chopped tarragon; 2 tablespoons snipped chives; 4 rib eye steaks, cut about 3/4 inch thick (about 10 ounces each); Salt and freshly ground black pepper