Cook the conchiglie in a large saucepan of boiling, salted water until 'al dente'; usually 8-10 minutes.
Meanwhile, heat the olive oil in a large frying pan over a moderate heat and sauté the mushrooms with a little seasoning, tossing and stirring occasionally, until softened. Continue to cook over a reduced heat for 3-4 minutes.
Drain the pasta, making sure you keep the cooking water. Bring the cooking water back to the boil and blanch the broccoli for 1 minute. Drain and toss with the pasta in the saucepan.
Stir in the mushrooms and spoon the pasta onto serving plates. Garnish with a pinch of the chilli flakes and season with salt and black pepper. Serve immediately.