Preheat the oven to 425 degrees F. Line a shallow baking dish with parchment paper. Set in the fish in a single layer. Drizzle with the oil; season with salt and pepper. Bake 12 to 15 minutes, or until just cooked through. While the fish cooks, place the lemon juice in a small skillet, set over medium heat and reduce by half. Add the whipping cream and reduce it by half. Add the dill, mussels and salt and pepper to taste. Cover and cook until the mussels open, about 2 to 3 minutes.
When cooked, divide the salmon among 4 plates; divide and arrange the mussels around the salmon and spoon over the sauce. Garnish with dill sprigs and serve.