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. Season with salt and pepper to taste.
Preheat the grill to medium-high.
Pat the salmon dry, brush with olive oil and season with salt and pepper. Grill for 12-15 minutes, flipping after 7, until cooked through.
Bring a large pot of salted water to a boil. Add the broccoli all at once and blanch for 1-2 minutes, until bright green. Drain and run under cold water to stop the cooking process.
To serve, divide the mashed potatoes between plates. Top with a salmon fillet and broccoli.