Bring a large pan of salted water to the boil and cook the orecchiette according to pack instructions, adding the broccoli for the final 3min of cooking time. Drain.
Meanwhile, heat oil in a large frying pan over medium heat. Squeeze the sausages out of their skins (discard skins). Add sausage meat to the pan in small pieces and fry for 7-8min, until browned and the sausage is cooked.
Stir the mustard and creme fraiche into the sausage pan, followed by the drained pasta and broccoli. Check seasoning. Sprinkle over chives and serve.