1.Bring a large pan of water to the boil, then add the broccoli. Boil for about 3 mins until bright green but not quite tender, then remove and cool under cold water. Drain well. Can be done up to a day ahead and kept covered in the fridge.
2.Combine the oil and butter in a large frying pan over a high heat. Once the butter is sizzling, add the mushrooms. Fry for 5 mins, stirring often, until golden.
3.Add the broccoli to the pan and toss together with the mushrooms. Cover the pan and cook for another 3 mins, shaking the pan now and again, until the broccoli stems are heated through and the mushrooms softened. Season well, then tip into a serving bowl, scatter with the cheese and drizzle with the oil, if you like.