How to Make It
Preheat the oven to 400°. In a medium enameled cast-iron casserole, combine the beets, vinegar, soy sauce, stock and 1/3 cup of the oil. Bring to a simmer. Cover and braise in the oven for about 1 hour, or until the beets are tender. Remove from the oven and let cool slightly. Peel the beets, cut them in wedges and return them to the braising liquid; keep warm. Leave the oven on.
In a small saucepan, bring the wine to a boil. Add the cream and return to a boil. Reduce the heat to moderate and cook until reduced by half. Remove from the heat and stir in the arugula. Season with salt and pepper and keep warm.
Heat the remaining 3 tablespoons of oil in a large ovenproof skillet. Season the salmon with salt and pepper and sear, skin side down, over high heat until the skin is crisp, about 1 minute. Turn carefully and sear 1 minute. Transfer to the oven and roast the salmon for about 3 minutes, or until medium rare and still bright pink in the center. Transfer to plates and spoon the arugula cream on top. Serve the beets alongside, drizzled with a little of their cooking liquid.