Preheat the oven to 375°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.
Pat the salmon dry, season with salt and pepper and arrange on a baking sheet. Roast for 12-15 minutes, until cooked through.
Combine all of the relish ingredients in a bowl.
To serve, divide the mashed potatoes and salmon between plates. Top with broccoli and relish.