Heat the butter and olive oil in a large, heavy-based frying pan. Fry the whole sage leaves for 30 seconds, drain and set aside.
Add the leeks and the shredded sage to your frying pan and fry over a low heat for 5-10 minutes or until the leeks are tender.
Meanwhile, bring a pan of water to the boil, add the sprouts and cook for 2-3 minutes until just tender (they should still feel quite firm). Drain and run under a cold tap until cool, then halve.
Add the sprouts and chestnuts to the pan, turn the heat to medium and fry for 2-3 minutes until they turn golden.
Season well and serve garnished with the remaining sage leaves.