Preheat the oven to 140C/280F/Gas 1. Grease an ovenproof dish.
Rinse the rice in a sieve under cold, running water until the water runs clear. Tip the rice into a saucepan.
Using the same liquid measuring jug you used to measure the rice, measure out double the amount of water and add it to the pan, along with the stock cubes and a little salt and freshly ground black pepper.
Bring the rice to the boil, cover and reduce the heat to a simmer. When the rice is nearly cooked, add the peas. Once the peas are cooked, drain the rice and peas and tip into the ovenproof dish.
Meanwhile, melt the butter in a frying pan, add the haddock and pour over enough milk to cover. Simmer until the haddock starts to fall apart.
Flake the haddock onto a plate, removing the bones.
Add the mustard to the rice mixture, mix in the grated cheese and the flaked haddock. Keep warm in the oven.
Meanwhile, fill a small pan just over one-third full with cold water and bring it to the boil. Add the vinegar and turn down to simmer. Crack the eggs one at a time into a small bowl and gently tip into the simmering water.
Lightly poach for 3-4 minutes. Remove with a slotted spoon and drain on kitchen towels.
Top the dish with the poached eggs to serve.