Preheat the oven to 400°F
In a large stockpot, place the potatoes and a generous pinch of salt. Cover with cold water and bring to a simmer. Cook at a simmer until the potatoes are fork-tender, about 15 minutes. Drain the potatoes and return to the pot. Add the butter, milk, buttermilk, salt and pepper. Mash until smooth. Fold in the horseradish and scallions. Season with salt and pepper to taste.
Combine the gremolata ingredients in a blender until mostly smooth. Season with salt and pepper.
Fill a saucepan with a metal steamer and 2 inches of water. Bring to a boil. Add the beets to the steamer basket and steam for about 10 minutes, or until very fork-tender.
Whisk together the shallot, lemon juice, rice wine vinegar, tamari, mustard and olive oil in a large bowl. Add the beets and half of the gremolata from the blender. Toss to coat.
Coat the salmon with the remaining gremolata on a baking sheet and roast until cooked through, 10-12 minutes.
Meanwhile, for the swiss chard, heat the oil in a large skillet over medium heat. Add the swiss chard and a pinch of salt and pepper and cook, stirring, until wilted.
To serve, divide the mashed potatoes, beet salad, salmon and swiss chard between plates.