Place the flour onto a large plate and season with salt and pepper.
Pat the fish dry then place in the flour to coat on both sides.
Heat one tablespoon of olive oil in a large frying pan with the butter then place the fish into the pan and cook over a medium heat until cooked through – this will take between 2-4 minutes each side depending on the size of the fillets.
Meanwhile, in a separate frying pan, melt the butter and add the mushrooms. Cook for around five minutes then pour in the wine and bring to the boil over a medium heat. Simmer for a few minutes before pouring in the cream. Simmer until the sauce thickens.
Stir in the lemon zest and juice and season. Stir in the dill.
Place the plaice fillets onto a plate, pour over some of the sauce. Add a few sprigs of fresh dill and a lemon wedge.Serve with tenderstem broccoli.