Sprinkle the salmon with salt and pepper. Place skin side up and rub 1 1/2 tablespoons softened butter all over the skin of the salmon. Transfer the salmon, buttered side up, to a sheet pan. Chill in the fridge to firm the butter, about 20 minutes.
Preheat the broiler to high.
Place the salmon about 5 inches from the heat source and cook until the skin is crispy and the fish is cooked through, 7 to 8 minutes.
In a small saucepan over moderate heat, whisk together the remaining 1 1/2 tablespoons butter, lemon zest, lemon juice, mustard and tarragon leaves. Divide the sauce between 2 plates and place 1 piece of salmon on top of each pool of sauce.
What Makes This Recipe Really Sing: This is the coolest way to get crispy skin on fish ever and the crispy skin is like a naturally salted and big flavored chip, so it's the best part!