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.