Fill your kettle and boil it. Set your oven to its lowest setting. Scrub the potatoes and chop them into small pieces around 1½ cm across. Tip them into a pan. Pour in enough boiling water to cover them, add a pinch of salt then pop a lid on the pan. Bring back up to the boil, then turn the heat down and simmer for 10-12 mins till the potatoes are tender when pierced with a fork or skewer.
While the potatoes cook, pick the leaves off the parsley sprigs and finely chop the leaves. Juice half the lemon into a small bowl. Set aside. Dust the flour onto a large plate and season with a pinch of salt and pepper. Dip the plaice fillets into the flour, coating them on both sides.
Warm a large frying pan on a medium-high heat, then add 1 tbsp olive oil and the plaice fillets, skinside down. Fry for 2-3 mins, then flip and fry for 2-3 mins more . The plaice should be opaque and flake easily when pressed with a fork. Transfer the plaice fillets to a plate and pop in the oven to keep warm. (If your frying pan is too small to cook all 4 fillets at once, fry 2 fillets in ½ tbsp olive oil, then transfer them to a plate and keep warm in the oven while you cook the other 2 fillets).
Take the pan off the heat and wipe clean with kitchen paper. Pop back on a low heat and add the butter. Swirl it round the pan to melt it. Add the lemon juice and chopped parsley. Add a pinch of salt and pepper and stir a few times to make a buttery sauce. Take off the heat.
The potatoes should be cooked by now. Drain them. Arrange the plaice fillets and potatoes on 2 warm plates. Drizzle over the lemon and parsley butter. Add a handful of rocket to each plate and serve with the remaining lemon sliced into wedges for squeezing.