Place the potatoes in a saucepan and cover with cold water. Bring to the boil over a medium-high heat with a lid on, then turn down and simmer for 15 minutes or until tender.
Drain the potatoes, then return them to the pan with 2 tbsp of chopped parsley and toss well. Season to taste and keep warm.
Pat the fish dry with kitchen paper. Heat a large non-stick pan over a medium-high heat. Add 10g of butter and 2 pieces of haddock (you will need to do this in two batches to prevent overcrowding the pan). Season to taste.
Once the fish has coloured nicely and become translucent on the bottom, carefully flip it over and season the other side. Continue to cook until the bottom side is also nicely coloured and cooked through. Keep these warm and repeat with the remaining 2 fillets.
Lower the heat and add the chopped shallots. Cook for 2 minutes until slightly softened. Meanwhile, add the spring greens to a pan of boiling water and cook for 2 minutes until just tender, then drain well.
Add the crème fraîche and mustard to the shallots then stir through the remaining parsley and lemon juice and season to taste. Add a splash of water, then stir the spring greens through.
Serve the fish on a bed of the creamy spring greens with the potatoes on the side. Add a wedge of lemon to garnish.