Melt butter in pre-heated saute pan. Add the vermouth and the juice of 1/2 lemon. Add halibut, salt and freshly ground black pepper.
Saute for 1 minute. Lower the heat, turn the halibut cheeks, cover and finish cooking on the other side, for a total cooking time of about 8 - 9 minutes per inch of thickness of the fish. Garnish with fresh dill.