Scrub the potatoes but keep them whole. Simmer in a pan of salted boiling water for 15 mins till they just start to soften. Drain and cool them under cold running water. Set aside.
Finely chop the dill leaves. Finely grate the zest from the lemon. Finely chop any thick spinach stalks. Shred the leaves. Measure out 1 tbsp of the butter into a bowl. Mash 1 tbsp flour into the butter with a fork.
Measure out 300 ml milk and pour into a pan. Bring it to the boil – stir constantly to stop the milk burning. When the milk is just boiling, add the floury butter. Lower the heat.
Whisk constantly for 8-10 mins till the sauce starts to thicken. When your whisk leaves trails in the sauce, take it off the heat. Stir in the dill, lemon zest, spinach leaves and stalks. Season.
Heat your oven to 180°C/Fan 160°C/Gas 4. Tip the fish pie mix into an ovenproof dish. Pour over the dill and spinach sauce. Stir carefully to mix.
Coarsely grate the potatoes into the pan you boiled them in. Add 1 tsp oil and some seasoning. Mix well. Spoon the potatoes over the fish. Bake in the oven for 30 mins till golden and bubbling.
Meanwhile, trim and peel the carrots. Slice into batons. Simmer the carrots in a pan of salted boiling water for 3-5 mins till they’re just soft when pierced with a fork. Roughly chop the parsley leaves.
Drain the carrots and tip them back into the pan. Add the remaining butter, the chopped parsley leaves and some salt and pepper. Toss to mix, then serve with the fish pie.