Preheat the oven to 140°C and grease an ovenproof dish.
Rinse the rice in a sieve under cold water until it runs clear.
Place rice in a pan with 360ml of water, stock cubes, salt, and pepper.
Boil the rice, then simmer covered, adding peas near the end of cooking.
Drain the rice and peas and transfer them to the ovenproof dish.
Melt butter in a frying pan and simmer the haddock in milk until it flakes.
Flake the haddock onto a plate while removing any bones.
Mix mustard, cheese, and flaked haddock into the rice and keep warm in the oven.
Bring a pan of water with vinegar to a simmer.
Poach the eggs for 4 minutes and drain on kitchen towels.
Serve the rice mixture topped with the poached eggs.