2 Tbsp extra virgin olive oil
2 large shallots, thinly sliced
2 lb mixed mushrooms, such as cremini, oysters, and shiitake, stemmed and thinly sliced
2 Tbsp Asian fish sauce
1 pinch of cayenne pepper
2 Tbsp chopped tarragon
2 Tbsp snipped chives
4 rib eye steaks, cut about 3/4-inch thick; about 10 ounce each
salt and freshly ground black pepper
In a large nonstick skillet, melt the butter in the 2 tablespoons of olive oil. Add the shallots and mixed mushrooms and cook over high heat, stirring occasionally, until the mushrooms are browned and their liquid is evaporated, about 8 minutes. Add the fish sauce and cayenne and cook for 1 minute. Stir in the tarragon and chives, cover and keep warm.
Preheat a grill pan. Brush the steaks with olive oil and season with salt and black pepper. Grill over moderately high heat for 3 to 4 minutes per side for medium-rare meat. Transfer the steaks to plates. Top with the mushrooms and serve.