Preheat the grill to medium. Rinse the fish fillets under cold running water and pat dry with kitchen paper. Season to taste with salt and pepper. Combine the olive oil with the drill and chives in a bowl, then brush the mixture over the fish. Transfer to the grill land cook for 6-8 minutes, turning once and brushing with more oil land herb mixture, until cooked to your taste.
Meanwhile, make the sauce. Put the egg yolks in a heatproof bowl over a saucepan of gently simmering water (or use a double boiler). Add water and season to taste with salt and pepper. Reduce the heat until the water in the saucepan is barely simmering and whisk constantly until the mixture begins to thicken. Whisk in the butter, one piece at a time, until the mixture is thick and shiny. Whisk in the lemon juice, then remove from the heat.
Remove the salmon from the grill and transfer to warmed individual serving plates. Pour the sauce over the fish and garnish with snipped fresh chives. Serve immediately on a bed of sprouting broccoli, garnished with sesame seeds.