Toss the salmon with the pepper and 1 tbsp dill and set aside.
Combine 2 cups water, 1 tbsp butter and the salt in a medium saucepan. Bring to a boil over a high heat and stir in the rice. Reduce the heat and simmer, covered, for 20 minutes until the water is absorbed and the rice is tender.
Melt the remaining 2 tbsp butter in a large frying pan over a medium heat. Add the onion and cook for about 3 minutes until soft.
Add the flour and cook, stirring, for about 2 minutes. Add the milk and the remaining dill and cook, stirring constantly, for about 2 minutes until the sauce thickens.
Reduce the heat, fold in the rice and cook until heated through. Transfer to a warm serving dish.
Arrange the salmon on top of the rice with the egg and lemon wedges. Sprinkle with parsley and dill and serve.