Heat two frying pansâ€”one with oil, and one with butter.
Dredge sole in flour, salt and pepper, then cook in oil for 2 minutes each side.
Cook mushrooms in butter for 4 minutes, then add to the fish.
Add remaining ingredients and simmer for 5 minutes.
Remove fish and place on heated platter, then pour sauce on top.
Serve with wedges of lemon.