How to Make It
Combine all of the ingredients and mix well.
Preheat the oven to 300°. On a rimmed baking sheet lined with aluminum foil, toss the sliced beets with 2 tablespoons of the olive oil; season with salt and pepper. Arrange the beets in a single layer and roast for about 1 hour, flipping the slices halfway through, until the beets are tender. Chop the beets and transfer to a large bowl.
Meanwhile, bring a medium saucepan of salted water to a boil. Add the rye berries and cook over moderate heat, stirring occasionally, until al dente, about 1 hour.
Drain the rye berries and add them to the bowl with the beets. Add the vinegar, horseradish and the remaining 3 tablespoons of olive oil, season with salt and pepper and toss to coat evenly. Keep warm.
In a small saucepan of boiling water, blanch the beet greens for 2 minutes. Drain and cool under cold water; pat dry. Chop the greens and toss with the beets and rye berries.
In a large cast-iron or nonstick skillet, heat the olive oil. Season the salmon fillets with salt and cook skin side down over moderately high heat until golden and crisp, about 4 minutes. Flip the fish and cook for 2 minutes. Add the butter and caraway seeds to the skillet and cook, basting with the caraway butter, until the salmon is just cooked through, about 1 minute longer.
Mound the rye berry salad on plates and spoon the dill sauce alongside. Top with the salmon, skin side up. Serve, passing the remaining dill sauce at the table.